Sum and Product of the Roots Quadratic Equations.
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Sum and Product of the Roots Quadratic Equations
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Transcript of Sum and Product of the Roots Quadratic Equations.
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 =
