1. Quadratic Equations
Sum and Product of the Roots

2. Solve for x by using the quadratic formula:
Aim: Use the sum and product of the roots in order to write a quadratic equation.
Solve for x by using the quadratic formula:
a. What is the sum of its roots? = -7
b. What is the product of its roots?
-3  -4 = 12

3. Sometimes you are given information backwards!
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.

4. Sum and Product of Roots for a Quadratic Equation
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:

5. The product 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:

6. Sum of roots = Product of roots =
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 = 1
b = 1
c =
-20
a. What is the sum of the roots? = = -1
b. What is the product of the roots? = =
-20

7. Sum of roots = Product of roots =
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
-b = 39
a. What is the sum of the roots?
b = -39
a = 20
b. What is the product of the roots?
c = - 80
c. What is the quadratic equation? 20 x2
-39 x
- 80
= y

8. Sum of roots = Product of roots =
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 = 10
b = - 10
(5 + 2i) + (5 – 2i) = 10
a = 1
b. What is the product of the roots?
(5 + 2i)  (5 – 2i) =
i – 10i – 4i2
c = + 29
25 – 4(-1) = 29
c. What is the quadratic equation? 1 x2
- 10 x
+ 29
= y

9. Sum of roots = Product of roots =
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 = 6
b = - 6
a = 1
b. What is the product of the roots?
c = + 7
c. What is the quadratic equation? 1 x2
- 6 x
+ 7
= y

10. Sum of roots = Product of roots =
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?
-b = 3
c = -2
b = - 3
a = 4
a = 2
( ) 2
a = 4 4 x2
- 3 x
- 2
= y

11. Sum of roots = Product of roots =
Aim: Use the sum and product of the roots in order to write a quadratic equation.
Sum of roots = Product of roots =
Find k such that -3 is a root of x2 + kx – 24 = 0.
Product =
Sum =