Solving Quadratic Equations by Factoring

Solving Quadratic Equations by Factoring - Transcript

Solve each equation by graphing 2 2 2x 2x 4 0 1 2 x 7 x 0

Day 4 Problems 2 1 07

3

x 3x 28
2

4

x 6x 9 0
2

4 x 2 7 x 15 0 5

6 3 Solving Quadratic Equations by Factoring Zero Product Property For any real numbers a and b if ab 0 then either a 0 b 0 or both a and b equal zero If x 5 x 7 0 then x 5 0 and or x 7 0

Two Roots
Solve each equation by factoring a

x 6x
2

x 6x
2

x 6x 0
2

x x 6 0

x 0 or

x 6 0

The solution set is 0 6

x 6

Two Roots
Solve each equation by factoring 2 b 2 x 7 x 15

2 x 7 x 15 2 2 x 7 x 15 0 2 x 3 x 5 0 2 x 3 0 or x 5 0 2x 3 x 5
2

3 5 The solution set is 2

3 x 2

Double Root
Solve

x 16 x 64 0 by factoring 2 x 16 x 64 0 x 8 x 8 0
2

x 8 0

or

x 8 0

x 8
The solution set is

x 8
8

What is the positive solution of the equation

Greatest Common Factor 2
B 2 C 5

A 4
2

3x 3x 60 0
D 10



3x 3x 60 0 2 3 x x 20 0 x x 20 0
2

x 4 x 5 0

x 4 0 or x 5 0 x 5 x 4
Since the question asked for the positive solution the answer is C

Write Quadratic Equations
When given the roots of a quadratic equation you can use the form x p x q 0 where p and q are the roots Use this pattern to find the quadratic equation for a given pair of roots

Write an equation with and 5 as its roots 2 Write the equation in the form ax2 bx c 0 where a b and c are integers

Write an Equation Given Roots 1

x p x q 0
1 x x 5 0 2
1 x x 5 0 2 9 5 2 x x 0 2 2

2 x2 9 x 5 0

More Practice
Textbook p 303 4 12 even 13 Homework Worksheet 6 3