Question

quiz 3.2.1 - solving quadratics by factoring
value: 3
solve for x.
$2x^2 - 2x - 4 = 0$
a. 5, 4
b. -1, 2
c. 1, -2
d. 6, -6

Explanation:

Step1: Simplify the quadratic equation

Divide all terms by 2:
$$\frac{2x^2}{2} - \frac{2x}{2} - \frac{4}{2} = \frac{0}{2}$$
$$x^2 - x - 2 = 0$$

Step2: Factor the quadratic

Find two numbers that multiply to -2 and add to -1:
$$(x - 2)(x + 1) = 0$$

Step3: Solve for x

Set each factor equal to 0:
$x - 2 = 0 \implies x = 2$
$x + 1 = 0 \implies x = -1$

Answer:

b. -1, 2