SUM AND PRODUCT OF ROOTS OF QUADRATIC EQUATION WORD PROBLEMS WORKSHEET

Problem 1 :

Find the sum and product of the roots of :

3x² – 2x + 7 = 0

Solution

Problem 2 :

Find the sum and product of the roots of :

x² + 11x - 13 = 0

Solution

Problem 3 :

Find the sum and product of the roots of :

 5x² – 6x - 14 = 0

Solution

Problem 4 :

The equation kx² – (1 + k)x + (3k + 2) = 0 is such that the sum of its roots is twice their product. Find k and the two roots.               Solution

Problem 5 :

The quadratic equation ax² – 6x + a - 2 = 0, a ≠ 0, has one root which is double the other.

a) Let the roots be α and 2α. Hence find two equations involving α.

b)  Find α and the two roots of the quadratic equation.

Problem 6 :

The quadratic equation kx² + (k–8)x + (1 – k) = 0, k ≠ 0, has one root which is two more than the other. Find k and the two roots.               Solution

Problem 7 :

The roots of the equation x² – 6x + 7 = 0 are α and β. Find the simplest quadratic equation with roots

α + 1/β and β + 1/α.

Solution

Problem 8 :

The roots of 2x² – 3x - 5 = 0 are p and q. Find all quadratic equations with roots p² + q and q² + p.

Solution

Problem 9 :

kx² + (k + 2) x - 3 = 0

has roots which are real and positive. Find the possible values that k may have.

Solution