OLGT: Solving Quadratic Equations
Do Now
Solve each equation. Decide whether
each equation is an identity, a
conditional or a contradiction.
1. 5(x+3) + 4x-5=-(2x-4)
2. -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
• Quadratic Formula
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
• Solve the quadratic equations
x2=17
2. (x-4)2=12
X=± 17
x-4 =± 12
x=4 ± 12
x=4 ± (4)(3)
x=4±2 3
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 = ± 24
• X =7± 24
• X=7± (4)(6)
• 7± 2 6
Homework
• Page 441 # 33-44