Question

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

Explanation:

Step1: Use root to factor form

If $m=-5$ is a root, then $(m+5)=0$; if $m=9$ is a root, then $(m-9)=0$.

Step2: Multiply the factors

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

Step3: Verify expansion (optional)

Expand the left side: $m^2 -9m +5m -45 = m^2 -4m -45=0$, which matches the roots.

Answer:

$\boldsymbol{(m + 5)(m - 9) = 0}$ (the first option)