Solve the equation. $8 p ^ { 2 } = - 32 p$
A) $\{ 4,0 \}$
B) $\{ 1,0 \}$
C) $\{ - 1,0 \}$
D) $\{ 4 \}$
E) $\{ - 4,0 \}$

Question

Quizplus · Accepted Answer

We start by factoring the equation:
$$8p^2=-32p$$
$$8p^2+32p=0$$
$$8p(p+4)=0$$
Then we use the zero product property: if the product of two factors is zero, at least one of the factors must be zero.
$$8p=0 \qquad \text{or} \qquad p+4=0$$
So we solve for $p$ in each equation:
$$p=0 \qquad \text{or} \qquad p=-4$$
Therefore, the solution set is $\{ -4,0 \}$, which corresponds to answer choice E.

Solve the Equation 8p2=−32p8 p ^ { 2 } = - 32 p8p2=−32p

Solve the Equation $8 p ^ { 2 } = - 32 p$