Quadratic Equations

Important Questions

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) 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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