Question

Find the values of x that make the following
quadratic equation equal 0: (𝑥 − 1)(2𝑥 + 5) = 0

Answer 1

To solve the equation \((x - 1)(2x + 5) = 0\), we can use the Zero Product Property, which states that if the product of two factors is zero, at least one of the factors must be zero.

This gives us two separate equations to solve:

1. \(x - 1 = 0\)
2. \(2x + 5 = 0\)

Now, we'll solve each equation:

1. For \(x - 1 = 0\):
\[
x = 1
\]

2. For \(2x + 5 = 0\):
\[
2x = -5 \\
x = -\frac{5}{2}
\]

So, the values of \(x\) that make the equation equal to 0 are:
\[
x = 1 \quad \text{and} \quad x = -\frac{5}{2}
\]