CBSE Class 10 Mathematics Quadratic Equation Worksheet Set J

CBSE Class 10 Quadratic Equation (3)

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1) Solve for x:

a) 9x2 – 9 (a + b) x + 2a2 + 5ab + 2b2 = 0 (2a+b/3, a + 2b/3)

b) 4x2 – 4a2x + (a4– b4) = 0 (a2 +b2)/2, (a2- b2)/2

c) 10ax2 – 6x +15ax – 9 = 0 (-3/2, 3/5a)

d) x2 – 2(a2 + b2 )x + (a2 – b2)2 = 0 (a + b)2, (a - b)2

e) √7x2 – 6x – 13 √7 (13√7/7, - √7)

f) 10x2 + 3bx + a2 - 7ax – b2

2) find the value of k so that the quadratic equation has equal roots:

a) 2kx2 – 40x + 25 = 0 (k = 8)

b) 2x2 – (k – 2) x + 1 = 0 ( 2 ± 2√2 )

c) ( k + 3 ) x2 + 2 ( k + 3 )x + 4 = 0 ( 1, - 3)

3) For what value of p the equation (1 + p) x2 + 2(1 + 2p) x + (1 + p) = 0 has coincident roots (0, -2/3)

4) Find the roots of the following quadratic equation by the method of completing the Square.

a) a2 x2 – 3abx + 2b2 = 0 (2b/a, b/a)

b) x2 – 4ax + 4a2- b2= 0

c) 6x2 – 7x + 2 = 0 (2/3, ½)

d) 4x2 + 4√3x + 3 = 0 ( ± √3/2)

5) Solve the following quadratic equations by factorization method:

a) 3x2 - 2√6x + 2 = 0 (√2/3, √2/3)

b) x2 - 5√5x + 30 = 0 (3√5, 2√5)

c) ax2 + a = a2x + x (a, 1/a)

6) write the nature of roots of quadratic equation: a) 4x2 + 4√3x + 3 = 0 b) x2 - b2 - a (2x – a) = 0

7) Check whether the equation x3 – 4x2 + 1 = (x – 2)2 is quadratic or not

8) Solve for x: 1 = 1 + 1 + 1 , a + b ≠ 0

a + b + x a b x (-a, -b)

9) If p, q are the roots of the equation x2 – 5x + 4 =0, find the value of 1 + 1 - 2pq

P q (-27/4)

10) Solve for x: x + x +1 = 34 (3/2, -5/2)

x + 1 x 15

11) Solve for x: 1 - 1 = 1 (7,-9)

x – 3 x + 5 6

12) If one root of a quadratic equation 3x2 + Px + 4 = 0 is 2/3, find the value of p (p = -8)

13) If x = √2 is a solution of quadratic equation x2 + k x – 4 = 0, then find the value of k ( k = √2)

14) Solve for x: 2 2x -1 – 3 x +3 = 5

X+3 2x-1 (-10, -1/5)

15) Solve the equation: 2(x – 3)2 + 3(x – 2) (2x – 3) = 8(x + 4) (x – 4) - 1 (x =5)

16) If the roots of the equation (b – c) x2 + (c – a) x + (a – b) = 0 are equal, then prove that 2b = a + c

17) The sum of the squares of two consecutive odd numbers is 394. Find the numbers. (13, 15)

18) Find two consecutive numbers, whose squares have the sum 85. (6, 7)

19) The product of 3 consecutive even numbers is equal to 20 times their sum. Find the numbers (6, 8, and 10)

20) The sum of the areas of two squares is 640 m2. If the difference in their perimeter is 64m .Find the sides of the two squares

(8m, 24m)

21) The difference of two numbers is 4. If the difference of their reciprocals is 4/21, find the numbers (3, 7)

22) The sum of two numbers is 15 and sum of their reciprocals is 3/10. Find the numbers (5, 10)

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