Question

Use the zero product property to find the solutions to the equation x2 – x – 6 = 0.
x = –3 or x = –2
x = –3 or x = 2
x = –2 or x = 3
x = 2 or x = 3

Answer 1

x² - x -6 = 0
Δ = b² -4ac = (-1)² -4·1·(-6) = 1 + 24 = 25
x₁= (-b + √Δ)/(2a) = (1 + √25)/2·1 = (1+5)/2 = 6/2 = 3
x₂= (-b - √Δ)/(2a) = (1 - √25)/2·1 = (1-5)/2 = -4/2 = -2

x=3 or x=-2

Answer 2

we know that

The Zero Product Property states that if $a*b = 0$ , then either $a = 0$ or $b = 0$ (or both)

we have

$x^{2} -x-6=0$

rewrite the expression

$x^{2} -x-6=(x+3)(x-2)$

so

$(x+3)(x-2)=0$

$(x+3)=0\\x=-3$

$(x-2)=0\\x=2$

therefore

the answer is the option

x = –3 or x = 2