Question

an equation has solutions of $m = -5$ and $m = 9$. which could be the equation?
$(m + 5)(m - 9) = 0$
$(m - 5)(m + 9) = 0$
$m^2 - 5m + 9 = 0$
$m^2 + 5m - 9 = 0$

Explanation:

Step1: Use zero product property

If $m=-5$ is a solution, then $m+5=0$. If $m=9$ is a solution, then $m-9=0$.

Step2: Form the equation

Multiply the two factors: $(m+5)(m-9)=0$

Step3: Verify other options (optional)

• For $(m-5)(m+9)=0$, solutions are $m=5$ and $m=-9$, which do not match.
• For $m^2-5m+9=0$, using quadratic formula $m=\frac{5\pm\sqrt{25-36}}{2}=\frac{5\pm\sqrt{-11}}{2}$, no real solutions matching the given values.
• For $m^2+5m-9=0$, using quadratic formula $m=\frac{-5\pm\sqrt{25+36}}{2}=\frac{-5\pm\sqrt{61}}{2}$, which are not $-5$ and $9$.

Answer:

A. $(m + 5)(m - 9) = 0$