Quadratic Equations

Important Questions

Q). Solve for x: , x ≠ 1, – , – 4 Ans: ∴ ∴ ∴ ∴ (8 x + 4) (x + 4) =…

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Q). If the zeroes of the polynomial x2 + p x + q are double in values to the zeros of 2 x2 – 5…

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Q).  If 𝛼 and β are zeroes of a polynomial x2 – 7 x + 10, then form a quadratic polynomial whose zeroes are 𝛼2 and…

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Q). Sum of the areas of two squares is 157 m2. If the sum of their perimeters is 68 m, find the sides of the…

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Q. In a fight of 600 km, an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by…

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Q)  The roots of equation (q – r) x² + (r – p) x + (p – q) = 0 are equal. Prove that: 2q…

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Q. A car travels a distance of 72 km at a certain average speed of X km per hour and then travels a distance of…

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Q) A brooch is a small piece of jewellery which has a pin at the back so it can be fastened on a dress, blouse or…

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Q) The speed of a motor boat is 20 km/hr. For covering the distance of 15 km the boat took 1 hour more for upstream…

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Q)  If a, b are the zeroes of polynomial f(x) = x2 – p (x + 1) – c then show that (a + 1)…

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Q) Amit is planning to buy a house and the layout is given below. The design and the measurement has been made such that areas of…

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Q) Basketball and soccer are played with a spherical ball. Even though an athlete dribbles the ball in both sports, a basketball player uses his hands…

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           Q) Write all the values of p for which the quadratic equation x2 + px +16 = 0 has equal…

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           Q) Find X in terms of a b, and c: , X ≠ a, b, c Ans: Given equation is:…

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(Q) The age of a man is twice the square of the age of his son. Eight years hence, the age of the man will…

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           Q) Find the value of ‘k’ for which the quadratic equation (k + 1) x2 – 6 (k + 1)…

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Q) A test consists of ‘True’ or ‘False’ questions. One mark is awarded for every correct answer while 1/4 mark is deducted for every wrong…

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Q) An asana is a body posture, originally and still a general term for a sitting meditation pose, and later extended in hatha yoga and…

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Q) A parabolic arch is an arch in the shape of a parabola. In structures, their curve represents an efficient method of load, and so…

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Q. Divide the polynomial x3 – 3 x2 + 5 x – 3 by x2 – 2 Ans: To divide the given polynomial, we can write…

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Q. Solve the quadratic equation: 2 X^2 – 7 X + 3 = 0 Ans: Given equation is: 2 X ^2 – 7 X +…

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           Q) Find the value of ‘k’ for which the quadratic equation (k + 1) x 2 – 2 (3 k +…

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Q)  Find the zeroes of the polynomial 4×2  + 4x – 3 and verify the relationship between zeroes and coefficients of the polynomial. Ans: In…

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Q)  If 𝛼, β are zeroes of quadratic polynomial x2 + x – 2, find the value of Ans: In the given polynomial equation f(x),…

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           Q) Find the value of ‘c’ for which the quadratic equation (c + 1) x2 – 6 (c + 1)…

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Q) A train travels a distance of 90 km at a constant speed. Had the speed been 15 km/h more, it would have taken 30…

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Q)  If 𝛼 and β are zeroes of a polynomial 6 x2 – 5 x + 1, then form a quadratic polynomial whose zeroes are…

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Q)  Find the zeroes of the quadratic polynomial x2 – 15 and verify the relationship between the zeroes and the coefficients of the polynomial. Ans:…

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Q) In a flight of 2800 km, an aircraft was slowed down due to bad weather. Its average speed is reduced by 100 km/h and…

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Q) A dealer sells an article for Rs. 75 and gains as much percent as the cost price of the article. Find the cost price…

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Q) Two water taps together can fill a tank in 3 hours. The tap of larger diameter takes 5 hours less than the smaller one to…

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Q) While playing in a garden, Samaira saw a honeycomb and asked her mother what is that. Her mother replied that it’s a honeycomb made by…

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Q) Tara scored 40 marks in a test, getting 3 marks for each right answer and losing 1 mark for each wrong answer. Had 4…

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Q)  A ball is thrown in the air so that t seconds after it is thrown, its height h metre above its starting point is…

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Q. Three years ago, Rashmi was thrice as old as Nazma. Ten years later, Rashmi will be twice as old as Nazma. How old are…

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Q)  Find the zeroes of the polynomial f(t) = t2 + 4 √3 t – 15 and verify the relationship between the zeroes and the…

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Q)  If 𝛼, β are zeroes of quadratic polynomial f(x) = 6 x2 + 11 x – 10, find the value of Ans: In the…

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Q. Solve for X : Ans: Given equation is: ∴ ∴ 4 (2 X + 3) – 5 X = 3 X (2X + 3) ∴…

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Q. The sum of two numbers is 18 and the sum of their reciprocals is 1/4 . Find the numbers. Ans: Let the numbers be X…

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Q. The sum of the reciprocals of Rehman’s ages (in years) 3 years ago and 5 years from now is 1/3 . Find his present…

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Q. In a class test, the sum of Shefali’s marks in Mathematics and English is 30. Had she got 2 marks more in Mathematics and…

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Q. The diagonal of rectangular field is 60 meters more than the shorter side. If the longer side is 30 m more than the shorter…

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Q. Is the following situation possible? If so, determine their present ages. The sum of the ages of two friends is 20 years. Four years…

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Q. Is it possible to design a rectangular park of perimeter 80m and the area  400 m2? If so, find the length and breadth. Ans: …

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Q. Is it possible to design a rectangular mango grove whose length is twice its breadth, and the area is 800 m2? If so, find…

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Q. Find the values of k for following quadratic equation, so that it has equal roots: kx (x -2) + 6 = 0 Ans:  Given…

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Q. Find the values of k for following quadratic equation, so that it has equal roots: 2×2 + kx + 3 = 0 Ans:  Let’s compare…

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Q. Sum of the areas of two squares is 468 m2. If the difference of their perimeters is 24 m, find the sides of the…

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Q. An express train takes 1 hour less than a passenger train to travel 132 km between Mysore and Bangalore (without taking into consideration the…

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Q. A train travels 360 km at a uniform speed. If the seed had been 5 km/h more, it would have taken 1 jour less…

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(Q) A rectangular floor area can be completely tiled with 200 square tiles. If the side length of each tile is increased by 1 unit, it…

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(Q) The difference of squares of two numbers is 180. The square of the smaller number is 8 times the larger number. Find the two…

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(Q) Rohan’s mother is 26 years older than him. The product of their ages (in years) 3 years from now will be 360. We would…

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(Q) A train travels a distance of 480 km at a uniform speed. If the speed had been 8 km / h less, then it…

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(Q) A cottage industry produces a certain number of pottery articles in a day. it was observed on a particular day that the cost of production…

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(Q) The altitude of a right angle triangle is 7 cm less than its base, If the hypotenuse is 13 cm, find the other two…

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(Q) Find the two consecutive positive integers, sum of whose squares is 365. Ans:  Let’s the 1st number be Next number has to be consecutive…

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(Q) A takes 6 days less than the time taken by B to finish a piece of work. If both A and B together can…

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(Q) A shopkeeper buys a number of books for Rs. 80. If he had bought 4 more for the same amount each book would have…

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Q) Solve the following quadratic equations by factorization method: Ans: Please do press “Heart” button if you liked the solution. 

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Q) Solve the following quadratic equations by factorization method: Ans: Please do press “Heart” button if you liked the solution. 

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Q) A train travels at a certain average speed for a distance 63 km and then travels a distance of 72 km at an average speed…

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Q) A train travels 360 km at a uniform speed. If the speed had been 5 km/hr more, it would have taken 1 hour less…

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Q)  Solve the following quadratic equation by factorization method: Ans: The Constant term can also be presented as: Similarly, Coefficient of the middle term can…

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Q)  Solve the following quadratic equation by factorization method: Ans: The Constant term can also be presented as: Similarly, Coefficient of the middle term can…

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Q)    Solve the following quadratic equation by factorization method: Ans: The Constant term can also be presented as: Similarly, Coefficient of the middle term…

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Q)    Solve the following quadratic equation by factorization method: Ans: Hence, x = -1, Since, it is given that x Hence, x = –…

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Q)    Solve the following quadratic equation by factorization method:  Ans: Please do press “Heart” button if you liked the solution. 

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Q) Solve the following quadratic equation by factorization method. Ans: Let’s find out the hidden quadratic equation: ∴  ∴  ∴ X (3 X – 5)…

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Q) If one root of the quadratic equation 2X2 + kX − 6 = 0 is 2, find the value of k. Also, find the other root. Ans: We…

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Q) If X = and X = − 3 are the roots of the equation aX2 + 7X + b = 0, find the values of…

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Q)  The graph of the polynomial – ax²+bx+c is shown below. Write the signs of ‘a’ and ‘b² – 4ac’. Ans: Clearly, f(x) = ax² +…

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Q)  Find the value of m for which the quadratic equation (m + 1) y2 – 6(m+1) y + 3(m+9) = 0, m ≠ -1…

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Q)  If 𝛼, β are zeroes of quadratic polynomial x2 – 2x + 3, find the polynomial whose roots are:1. 𝛼 + 2, 𝛽 +…

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Q) Raj and Ajay are very close friends. Both the families decide to go to Ranikhet by their own cars. Raj’s car travels at a…

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Q) Two water taps together can fill a tank in 9 hours. The tap of larger diameter takes 10 hours less than the smaller one to…

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Q) A motor boat whose speed is 18 km/h in still water takes 1 hour more to go 24 km upstream than to return downstream to…

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Q)  If 𝛼, β are zeroes of quadratic polynomial 5×2 + 5x + 1, find the value of1. 𝛼2 + 𝛽22. 𝛼‾1 + 𝛽‾1 Ans: Given polynomial equation…

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Q)  In a pool at an aquarium, a dolphin jumps out of the water travelling at 20 cm per second. Its height above water level…

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Q)  Find the value of ‘p’ for which one root of the quadratic equation px2 – 14x + 8 = 0 is 6 times the…

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Q)  Find the discriminant of the quadratic equation 4×2 – 5 = 0 and hence comment on the nature of the equation. Ans: Given equation is…

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Q)  Find the value of ‘p’ for which the quadratic equation px (x – 2) + 6 = 0 has two equal roots. Ans:  Given…

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Q)  Find the sum and product of the roots of the quadratic equation 2×2 – 9x + 4 = 0. Ans:  We know that sum…

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Q)  If one zero of the polynomial p(x) = 6×2 + 37 x – (k-2) is reciprocal of the other, then find the value of…

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Q)Jaya scored 40 marks in a test getting 3 marks for each correct answer and losing 1 mark for each incorrect answer., Had 4 marks…

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Q) Half of the difference between two numbers is 2. The sum of the greater and twice the smaller number is 13. Find the numbers.…

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