Question

Solve the quadratic equation: 3x2 − 2x − 8 = 0

Answer 1

Solutions 

Factor 3x²−2x−8

1. Multiply 3 by -8, which is -24.

2. Ask: Which two numbers add up to -2 and multiply to -24?

3. Answer: 4 and -6

4. Rewrite −2x as the sum of 4x and −6x: 

$3x^2+4x-6x-8=0$

Factor out common terms in the first two terms, then in the last two terms 

$x(3x+4)-2(3x+4)=0$ 

 Factor out the common term 3x+4 

$(3x+4)(x-2)=0$ 

Solve for x

1. Ask: When will (3x+4)(x−2) equal zero?

2. Answer: When 3x+4=0 or x−2=0.

3. Solve each of the 2 equations above: 

x = −4 / 3,2

Answer 2

$3x^2-2x-8=0\\ 3x^2-6x+4x-8=0\\ 3x(x2)+4(x-2)=0\\ (3x+4)(x-2)=0\\ x=-\dfrac{4}{3} \vee x=2$