Quadratic Equations
Important Questions
Q) The sum of the squares of two consecutive natural numbers is 365. Find the numbers. Ans: Step 1: Let…
Q) Solve the quadratic equation 2×2 – 3x – 5 = 0 using the quadratic formula. Ans: [Approach: we know that…
Q) Find the value of ‘c’ for which the quadratic equation (c + 1) y 2 – 6 (c +…
Q). Solve for x: , x ≠ 1, – , – 4 Ans: ∴ ∴ ∴ ∴ (8 x + 4) (x + 4) =…
Q). If the zeroes of the polynomial x2 + p x + q are double in values to the zeros of 2 x2 – 5…
Q). If 𝛼 and β are zeroes of a polynomial x2 – 7 x + 10, then form a quadratic polynomial whose zeroes are 𝛼2 and…
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…
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…
Q) The roots of equation (q – r) x² + (r – p) x + (p – q) = 0 are equal. Prove that: 2q…
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…
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…
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…
Q) If a, b are the zeroes of polynomial f(x) = x2 – p (x + 1) – c then show that (a + 1)…
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…
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…
Q) Write all the values of p for which the quadratic equation x2 + px +16 = 0 has equal…
Q) Find X in terms of a b, and c: , X ≠ a, b, c Ans: Given equation is:…
(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…
Q) Find the value of ‘k’ for which the quadratic equation (k + 1) y2 – 6 (k + 1)…
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…
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…
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…
Q. Divide the polynomial x3 – 3 x2 + 5 x – 3 by x2 – 2 Ans: To divide the given polynomial, we can write…
Q. Solve the quadratic equation: 2 X^2 – 7 X + 3 = 0 Ans: Given equation is: 2 X ^2 – 7 X +…
Q) Find the value of ‘k’ for which the quadratic equation (k + 1) x 2 – 2 (3 k +…
Q) Find the zeroes of the polynomial 4×2 + 4x – 3 and verify the relationship between zeroes and coefficients of the polynomial. Ans: In…
Q) If 𝛼, β are zeroes of quadratic polynomial x2 + x – 2, find the value of Ans: In the given polynomial equation f(x),…
Q) Find the value of ‘c’ for which the quadratic equation (c + 1) x2 – 6 (c + 1)…
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…
Q) If 𝛼 and β are zeroes of a polynomial 6 x2 – 5 x + 1, then form a quadratic polynomial whose zeroes are…
Q) Find the zeroes of the quadratic polynomial x2 – 15 and verify the relationship between the zeroes and the coefficients of the polynomial. Ans:…
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…
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…
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…
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…
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…
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…
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…
Q) Find the zeroes of the polynomial f(t) = t2 + 4 √3 t – 15 and verify the relationship between the zeroes and the…
Q) If 𝛼, β are zeroes of quadratic polynomial f(x) = 6 x2 + 11 x – 10, find the value of Ans: In the…
Q. Solve for X : Ans: Given equation is: ∴ ∴ 4 (2 X + 3) – 5 X = 3 X (2X + 3) ∴…
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…
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…
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…
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…
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…
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: …
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…
Q. Find the values of k for following quadratic equation, so that it has equal roots: kx (x -2) + 6 = 0 Ans: Given…
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…
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…
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…
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…
(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…
(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…
(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…
(Q) A train travels a distance of 480 km at a uniform speed. If the speed had been 8 km / h less, then it…
(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…
(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…
(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…
(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…
(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…
Q) Solve the following quadratic equations by factorization method: Ans: Please do press “Heart” button if you liked the solution.
Q) Solve the following quadratic equations by factorization method: Ans: Please do press “Heart” button if you liked the solution.
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…
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…
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…
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…
Q) Solve the following quadratic equation by factorization method: Ans: The Constant term can also be presented as: Similarly, Coefficient of the middle term…
Q) Solve the following quadratic equation by factorization method: Ans: Hence, x = -1, Since, it is given that x Hence, x = –…
Q) Solve the following quadratic equation by factorization method: Ans: Please do press “Heart” button if you liked the solution.
Q) Solve the following quadratic equation by factorization method. Ans: Let’s find out the hidden quadratic equation: ∴ ∴ ∴ X (3 X – 5)…
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…
Q) If X = and X = − 3 are the roots of the equation aX2 + 7X + b = 0, find the values of…
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 +…
Q) Find the value of m for which the quadratic equation (m + 1) y2 – 6(m+1) y + 3(m+9) = 0, m ≠ -1…
Q) If 𝛼, β are zeroes of quadratic polynomial x2 – 2x + 3, find the polynomial whose roots are:1. 𝛼 + 2, 𝛽 +…
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…
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…
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…
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…
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…
Q) Find the value of ‘p’ for which one root of the quadratic equation px2 – 14x + 8 = 0 is 6 times the…
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…
Q) Find the value of ‘p’ for which the quadratic equation px (x – 2) + 6 = 0 has two equal roots. Ans: Given…
Q) Find the sum and product of the roots of the quadratic equation 2×2 – 9x + 4 = 0. Ans: We know that sum…
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…
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…
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.…