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OLGT: Solving Quadratic Equations - PowerPoint PPT Presentation

OLGT: Solving Quadratic Equations. Do Now Solve each equation. Decide whether each equation is an identity, a conditional or a contradiction. -5(x+3 ) - 4x-5=-(9x-4 ) -6(2x+1)-3(x-4)=-15+1. Using the Zero-Factor Property. A quadratic equation written in standard form is

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Presentation Transcript

Do Now

Solve each equation. Decide whether each equation is an identity, a conditional or a contradiction.

-5(x+3) - 4x-5=-(9x-4)

-6(2x+1)-3(x-4)=-15+1

Using the Zero-Factor Property
• A quadratic equation written in standard form is
• Ax2+bx+c = 0, where a, b, c are real numbers and a can not equal zero.
• You can solve them by using one of the three methods
• Zero-factor Property
• Square Root Property
Zero-Factor Property
• Solve 6x2+7x=3
• First put in standard form
• 6x2+7x-3=0
• Then factor
• (3x-1)(2x-3)=0
Zero-Factor Property
• Apply the zero-factor property
• 3x-1=0 or 2x+3=0
• 3x=1 2x=-3
• X=1/3 x=-3/2
• Check
• 6(1/3)2+7(1/3)=3 and
• 6(-3/2)2+7(-3/2)=3
Using the Square Root Property

1. x2=17 2. (x-4)2=12

X= x-4 =

x=4 x= x=4

Solve by the zero-property
• -6x2+7x = -10
• -6x2+7x + 10 = 0
• -1(6x2-7x - 10)=0
• -1(6x+5)(x-2) =0
• 6x-5=0 or x-2 =0
• 6x=5
• X=5/6 or x=2
Square Root Property
• (x-7)2=24
• X-7 =
• X =7
• X=7
• 7
Try these
• 1
• (x+4) (x-2) = 0
• X = -4 or x = 2
• ( 2x + 5) (x-3) = 0
• 2x+5 = 0 x-3=0
• X= -5/2 x= 3
• x2+ 2x -8 = 0
• 2x2- x -15 = 0

1. X2 = 25

• X =
• X = 5
• 2. ( 3x-1) 2 =12
• 3x – 1 =
• 3x = 1
• x = 1
• 3
Homework
• Page 441 # 33-44