While using the Zero Product Property to find the values of x that make the quadratic equation (x+3)(x+4) equals 0, Oliver completed the work provided in the table. Is Oliver’s work accurate?

Answer 1

To determine if Oliver's work is accurate, let's examine each step.

Oliver started with the quadratic equation (x+3)(x+4) = 0.

Next, he applied the Zero Product Property, which states that if a product of two factors equals zero, then at least one of the factors must equal zero. So, he set each factor equal to zero:

(x + 3) = 0 and (x + 4) = 0.

Next, Oliver solved each equation individually:

x + 3 = 0 ---> x = -3

x + 4 = 0 ---> x = -4

Let's check these values:

If we substitute x = -3 into the quadratic equation, we get:

(-3 + 3)(-3 + 4) = 0
(0)(1) = 0
0 = 0

This checks out. Similarly, if we substitute x = -4:

(-4 + 3)(-4 + 4) = 0
(-1)(0) = 0
0 = 0

This also checks out.

Therefore, Oliver's work is accurate. The values x = -3 and x = -4 make the quadratic equation (x+3)(x+4) equal to 0.

Answer 2

Based on the Zero Product Property, which of the following statements must be true about the quadratic equation (2x−3)(x+2)=0 ?

Answer 3

According to the Zero Product Property, if a product of two factors equals zero, then at least one of the factors must equal zero.

In the given quadratic equation (2x−3)(x+2) = 0, we can apply the Zero Product Property to determine the possible values of x.

Setting the first factor equal to zero: 2x - 3 = 0

Solving for x:
2x = 3
x = 3/2

Setting the second factor equal to zero: x + 2 = 0

Solving for x:
x = -2

Therefore, based on the Zero Product Property, the equation (2x−3)(x+2) = 0 implies that either x = 3/2 or x = -2 must be true.