WORKSHEET ON QUADRATIC EQUATIONS CLASS 10 CBSE

1. If x = 2 and x = 3 are the roots of the equation

3x² - 2kx + 2m = 0,

find the value of k and m.

2. If one root of the quadratic equation 2x² + kx - 6 = 0, find the value of k. Also find the other root.

3. Solve the following quadratic equation by factorization method.

(i) (4/x) - 3 = 5/(2x + 3).

(ii) 4x² - 2(a² + b²)x + a²b² = 0

(iii) (2/x²) - (5/x) + 2 = 0

(iv) [1/(x - 2)] + [2/(x - 1)] = 6/x

4. Determine whether the given quadratic equation has real roots and if so, find the roots.

6x² + x - 2 = 0

5. Find the values of k for which the given equation has real and equal roots.

x² - 2x(1 + 3k) + 7(3 + 2k) = 0

6. Find the values o f k for which the following equation has equal roots.

(k - 12)x² + 2(k - 12) + 2 = 0

7. The sum of two numbers is 15. If the sum of the their reciprocals is 3/10, find the numbers.

8. Find two consecutive numbers whose squares have the sum 85.

9. Two numbers differ by 3 and their product is 504. Find the numbers.

10. The sum of two numbers is 18. The sum of their reciprocals is 1/4. Find the numbers.

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