### Home > INT2 > Chapter 5 > Lesson 5.2.5 > Problem5-122

5-122.

Use the Zero Product Property to solve for the $x$-intercepts of the parabolas represented below.

1. $y = 3x^2 − 7x + 4$

One of the factors is $(x −1)$, find the other one.

1. $(x + 5)(−2x + 3) = y$

According to the Zero Product property,
if $(x + 5)(−2x + 3) = 0$ then either
$(x + 5) = 0$ or $(−2x + 3) =$0.

1. $x^2 + 6x = y$

After factoring, this equation becomes $x(x + 6) = y$.
Now apply the Zero Product Property.

1. $y = 3(x − 5)(2x + 3)$

$x=5 \text { or } x = -\frac{3}{2}$

$\text{ The two } x\text{-intercepts are } (5,0) \text { and } \left ( -\frac{3}{2},0 \right ).$