Sect' 6'3 Solving Quadratic Equations by Factoring

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Sect. 6.3 Solving Quadratic Equations by
Factoring
Goal 1 Solve Quadratic Equations by
Factoring Goal 2 Write a Quadratic Equation
with Given Roots
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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 0
If (x 2)(x 7) 0, then x - 2 0 or x 7 0
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Many of the simpler quadratic equations with
rational roots can be solved by factoring.
1. Start with the equation in the form    
ax2 bx c 0                        (be
sure it is set equal to zero!)
2. Factor the left hand side (assuming zero is
on the right)
3. Set each factor equal to zero
4. Solve to determine the roots (the values of x)
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Solve by Factoring
3x(x 2) 0
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Solve by Factoring
x2 7x 12 0
x - 4 or x - 3
- 4, - 3
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Solve by Factoring
x2 6x - 9
x 3
3
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Solve by Factoring
3x2 5x 2
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Writing Quadratic Equations
A Quadratic equation of the form (x p)(x q)
0 has roots p and q
You can use this pattern to find a quadratic
equation for a given pair of roots
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Write the quadratic equation with the following
roots. Write in the form ax2 bx c 0
where a, b, and c are integers
Roots are 3 and 4
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Write the quadratic equation with the following
roots. Write in the form ax2 bx c 0
where a, b, and c are integers
3x2 16x 12 0