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.

 1)   -5 and 62)  4 and -103)  -3 and 4 4)  -5/3 and -35)  7/5 and 26)  3 and -70

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

Problem 3 :

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

2kx2 – 20x + 21 = 0 is 2

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)

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.

 1) k = 32) P = -6, 63)  k = -25/2, 2 4)  k = 256/95)  k = -25, 26)  k = 9/87)  a = -2, b = 2

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