Solving Quadratic Equations (3 methods)

Solve
x² + 2x - 24 = 0

• x = -6, x = 4
• x = 6, x = -4
• x = 12, x = -2
• x = 8, x = -3

Solve x^2 - 3x - 4 = 0 using the best method.

• x = 4 and -1

• x = -4 and -1

• x = 4 and 1

• x = -4 and 1

• -2, 4
• -8
• ±8
• No real solution

Solve the equation using the zero product property.

3x(2x - 4) = 0

• x = -1/3 or x = -2

• x = 0 or x = 2

• x = 0 or x = -2

• x = -1/3 or x = 2

Solve
16a² - 9 = 0

• a = ^-3/₄, ³/₄ 
• a = ^-4/₃, ⁴/₃ 
• a = ^-9/₁₆, ⁹/₁₆ 
• a = ^-16/₉, ¹⁶/₉ 

Solve by finding square roots and simplify completely:
 $2x^2=20$ 

•  $x=\pm10$  

•  $x=\sqrt{10}$  

•  $x=\pm\sqrt{10}$  

• No real solutions

Solve using the Quadratic Formula:
 $x^2-7x+10=0$ 

•  $x=2\ or\ x=5$  

•  $x=-2\ or\ x=-5$  

•  $x=4\ or\ x=10$  

• No real solutions

Solve using the Quadratic Formula:
 $5x^2+3x-1=0$ 

•  $x=\frac{3\pm\sqrt{29}}{5}$  

•  $x=\frac{8}{5}\ or\ x=-\frac{2}{5}$  

•  $x=\frac{-3\pm\sqrt{29}}{10}$  

• No real solutions

When does a quadratic equation have no real solutions?

• When you cannot factor it

• When it begins with a negative leading coefficient

• When there is a square root of a negative number

• When it only has two terms

 $3x^2-2x-5=0$  Use Quadratic Formula to solve:

•  $x=\frac{1\pm\sqrt{265}}{12}$  

•  $x=\frac{5}{3}\ and\ x=-1$  

•  $x=\frac{2\pm8}{6}$  

•  $\left(3x-5\right)\left(x+1\right)$