Question

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

Answer 1

To find the values of \( x \) that satisfy the equation \((x-1)(2x+5) = 0\), we can use the zero product property. This property states that if the product of two factors equals zero, at least one of the factors must equal zero.

We set each factor equal to zero:

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

Now, we solve each equation.

**For the first equation:**
\[
x - 1 = 0 \\
x = 1
\]

**For the second equation:**
\[
2x + 5 = 0 \\
2x = -5 \\
x = -\frac{5}{2}
\]

Thus, the solutions to the equation \((x-1)(2x+5) = 0\) are:
\[
x = 1 \quad \text{and} \quad x = -\frac{5}{2}
\]