FIND SUM AND PRODUCT OF ROOTS OF A QUADRATIC EQUATION WORKSHEET

Problem 1 :

Find the sum and product of roots of the quadratic equation

x² + 5x + 6 = 0

Solution

Problem 2 :

Find the sum and product of roots of the quadratic equation

x² - 4x - 10 = 0

Solution

Problem 3 :

Find the sum and product of roots of the quadratic equation

2x² + 6x + 8 = 0

Solution

Problem 4 :

Find the sum and product of roots of the quadratic equation

3x² + 5x - 9 = 0

Solution

Problem 5 :

Find the sum and product of roots of the quadratic equation

5x² - 7x - 10 = 0

Solution

Problem 6 :

Form the equation whose roots are 7and -10.

Solution

Find all values of k for which the equation has

(a) two solutions

(b) one solution and

(c) no solutions.

Problem 7 :

2x² + x + 3k = 0

Solution

Problem 8 :

x² − 4kx + 36 = 0

Solution

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

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

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.

Solution

Problem 6 :

Find the values of k for each of the following quadratic equations, so that they have two equal roots.

(i) 2x² + kx + 3 = 0

(ii) kx (x – 2) + 6 = 0

Solution