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Home > INT2 > Chapter 5 > Lesson 5.2.5 > Problem 5-122

5-122.

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

$y = 3x^2 − 7x + 4$
Hint (a):
One of the factors is $(x −1)$ , find the other one.

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

$x^2 + 6x = y$
Hint (c):
After factoring, this equation becomes $x(x + 6) = y$ .
Now apply the Zero Product Property.

$y = 3(x − 5)(2x + 3)$
Answer (d):
$x=5 \text { or } x = -\frac{3}{2}$
The two $x$ -intercepts are $\left(5,0\right)$ and $\left(-\frac{3}{2},0\right)$ .

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