Quadratic Equations Sum and Product of the Roots

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? -3 + -4 = -7 b. What is the product of its roots? -3  -4 = 12

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.

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:

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:

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

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

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) = 25 + 10i – 10i – 4i2 c = + 29 25 – 4(-1) = 29 c. What is the quadratic equation? 1 x2 - 10 x + 29 = y

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

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

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 =