Solving Quadratics

Factor and Solve

6x² + 17x + 12 = 0

• x = -4/3, x = -3/2

• x = 9, x = 8

• x = 4, x = 3

• x = -4, x = -3

What is the greatest number of solutions that a Quadratic Equation can have?

• 0

• 1

• 2

• 3

Solve the equation using the zero product property.
(x- 9)(x + 3) = 0

• x = 3 or x = 9

• x = 3 or x = -9

• x + -3 or x = 9

• x = -3 or x = -9

What is the first question you ask yourself when factoring a polynomial? 

• How many terms does it have? 

• Is there a GCF? 

• What strategy should I use? 

• Why do I have to learn this?!?!?!

What is the first step in solving 
(x + 2)(x - 3) = 0      ?

• Plug in zero for x

• Solve for x

• FOIL

• Set each binomial factor equal to zero

Solve:  $2x^2-x-15=0$  

•  $x=-\frac{5}{2}$  and  $x=3$  

•  $x=\frac{5}{2}$  and  $x=-3$  

•  $x=\frac{5}{2}$  and  $x=3$  

•  $x=-\frac{5}{2}$  and  $x=-3$  

Solve:   $3x^2=9x$  

•  $x=3$  and  $x=-3$  

•  $x=3$  

•  $x=0$  and  $x=9$  

•  $x=0$  and  $x=3$  

Solve:   $4x^2+15x+14=0$  

•  $x=\frac{7}{4}$  and  $x=2$  

•  $x=-\frac{7}{4}$  and  $x=2$  

•  $x=\frac{7}{4}$  and  $x=-2$  

•  $x=-\frac{7}{4}$  and  $x=-2$  

What are the factors of

25x² - 81?

• (5x - 9)(5x + 9)

• (5x - 9)(5x - 9)

• (5x + 9)(5x + 9)

• Prime (Can't be factored)

What should you do first in solving this equation?

x² + 6x - 13 = 3

• Get factored form

• Write down: a=1, b=6, c=-13

• Make it equal 0 by subtracting 3 on each side

• Type it all in a calculator.