Question

Solve using zero product property

A^2 - 7a+10=0

Answer 1

To solve the equation \( A^2 - 7A + 10 = 0 \) using the zero product property, we need to factor the quadratic expression.

1. We start by finding two numbers that multiply to \( 10 \) (the constant term) and add up to \( -7 \) (the coefficient of the linear term).
- The numbers are \( -5 \) and \( -2 \), since:
\[
-5 \times -2 = 10
\]
\[
-5 + (-2) = -7
\]

2. We can now factor the quadratic:
\[
A^2 - 7A + 10 = (A - 5)(A - 2)
\]

3. Now, set the factors equal to zero:
\[
(A - 5) = 0 \quad \text{or} \quad (A - 2) = 0
\]

4. Solve each equation:
- For \( A - 5 = 0 \):
\[
A = 5
\]
- For \( A - 2 = 0 \):
\[
A = 2
\]

Thus, the solutions are:
\[
A = 5 \quad \text{and} \quad A = 2
\]