Question

solve the equation.
$q^2 - q - 2 = 0$
$q = \square$
(use a comma to separate answers as needed.)

Explanation:

Step1: Factor the quadratic equation

We need to factor \( q^2 - q - 2 = 0 \). We look for two numbers that multiply to \(-2\) and add up to \(-1\). The numbers are \(-2\) and \(1\) because \((-2)\times1=-2\) and \(-2 + 1=-1\). So we can factor the equation as:
\( (q - 2)(q + 1)=0 \)

Step2: Solve for \( q \) using zero - product property

The zero - product property states that if \( ab = 0 \), then either \( a = 0 \) or \( b = 0 \).
For \( (q - 2)(q + 1)=0 \), we set each factor equal to zero:

• If \( q - 2=0 \), then \( q=2 \) (by adding 2 to both sides of the equation).
• If \( q + 1=0 \), then \( q=-1 \) (by subtracting 1 from both sides of the equation).

Answer:

\(2, - 1\)