FIND SUM AND PRODUCT OF ROOTS OF A QUADRATIC EQUATION WORKSHEET

Find the sum and product of roots of the quadratic equations given below.

1)  x² + 5x + 6 = 0

2)  x² - 4x - 10 = 0

3)  2x² + 6x + 8 = 0

4)  3x² + 5x - 9 = 0

5)  5x² - 7x - 10 = 0

6)  Form the equation whose roots are 7and -10.

Problem 1 :

Find k if the difference between the roots of the quadratic equation

x² – 4x + k = 0 is 2

Solution

Problem 2 :

Find the value of p such that the difference of the roots of the equation

x² – px + 8 = 0 is 2

Solution

Problem 3 :

Find the value of k such that the difference of the roots of the equation

2kx² – 20x + 21 = 0 is 2

Solution

Problem 4 :

Find k so that one root of the equation 2x² – 16x + k = 0 is twice the other. (Hint : One root = α, Other root = 2α)

Solution

Problem 5 :

Find k so that one root of the equation

k(x – 1)² = 5x – 7

is twice the other.                 Solution

Problem 6 :

Find k so that the roots of the quadratic equation

2x² + 3x + k = 0

are equal.                        Solution

Problem 7 :

If 1 – i and 1 + i are the roots of the equation

x² + ax + b = 0

where a, b ∈  r, then find the values of a and b.

Solution