Sum and Product of the Roots

Quadratic Equations

Solve for x by using the quadratic formula:

a. What is the sum of its roots?

b. What is the product of its roots?

-3 + -4 = -7

-3 -4 = 12

Aim: Use the sum and product of the roots in order to write a quadratic equation.

• Sometimes you are given information backwards!

• You may be given information and asked to write a quadratic equation.

• Remember – it’s all about finding which factors of ac add to b.

Aim: Use the sum and product of the roots in order to write a quadratic equation.

Sum and Product of Roots for a Quadratic Equation

The sum of the roots is:

Aim: Use the sum and product of the roots in order to write a quadratic equation.

The product of the roots is:

Aim: Use the sum and product of the roots in order to write a quadratic equation.

Sum of roots = Product of roots =

Given the equation x2 + x – 20 = 0,

a. What is the sum of the roots?

b. What is the product of the roots?

a = b = c =1 -20

= -1

1

= -20

Aim: Use the sum and product of the roots in order to write a quadratic equation.

=

=

Sum of roots = Product of roots =

The roots of a quadratic are and

a. What is the sum of the roots?

b. What is the product of the roots?

c. What is the quadratic equation?

20 x2 -39 x - 80= y

b = -39

a = 20

c = - 80

-b = 39

Aim: Use the sum and product of the roots in order to write a quadratic equation.

Sum of roots = Product of roots =

The roots of a quadratic are 5 + 2i and 5 – 2i.

a. What is the sum of the roots?

b. What is the product of the roots?

c. What is the quadratic equation?

(5 + 2i) + (5 – 2i) = 10

(5 + 2i) (5 – 2i) = 25 + 10i – 10i – 4i2 25 – 4(-1) = 29

b = - 10

a = 1

c = + 29

x2 x = y

-b = 10

Aim: Use the sum and product of the roots in order to write a quadratic equation.

1 - 10 + 29

Sum of roots = Product of roots =

The roots of a quadratic are and .

a. What is the sum of the roots?

b. What is the product of the roots?

c. What is the quadratic equation?

b = - 6

a = 1

c = + 7

-b = 6

x2 x = y- 61 + 7

Aim: Use the sum and product of the roots in order to write a quadratic equation.

Sum of roots = Product of roots =

The sum of the roots of a quadratic is , the product of the

roots is . What is the equation of the quadratic?

a = 4

-b = 3b = - 3

x2 x = y

Aim: Use the sum and product of the roots in order to write a quadratic equation.

a = 2( ) 2a = 4c = -2

4 - 3 - 2

Sum of roots = Product of roots =

Find k such that -3 is a root of x2 + kx – 24 = 0.

Aim: Use the sum and product of the roots in order to write a quadratic equation.

Product = Sum =