An equation has solutions of m = –5 and m = 9. Which could be the equation?

A. (m + 5)(m – 9) = 0
B. (m – 5)(m + 9) = 0
C. m² – 5m + 9 = 0
D. m² + 5m – 9 = 0

The correct equation that has solutions of m = − 5 and m = 9 is option A: ( m + 5 ) ( m − 9 ) = 0 . This can be confirmed by expanding the factored equation into standard form. The other options do not produce the given solutions.
;

Answered by Anonymous | 2025-07-04

To solve this question, we need to identify which equation has solutions of m = − 5 and m = 9 .
When an equation has these solutions, it indicates that the equation can be expressed as a product of factors set equal to zero. The factors should be ( m + 5 ) and ( m − 9 ) , because if you substitute m = − 5 , the first factor becomes zero, and if you substitute m = 9 , the second factor becomes zero.
Let's examine the given options:
A. ( m + 5 ) ( m − 9 ) = 0
This setup describes two solutions, m = − 5 and m = 9 , because each factor independently becomes zero when m takes these values. Therefore, this option is correct.
B. ( m − 5 ) ( m + 9 ) = 0
This would have solutions m = 5 and m = − 9 , which are not the solutions we are looking for.
C. m 2 − 5 m + 9 = 0
The factors of this equation do not correlate with m = − 5 and m = 9 .
D. m 2 + 5 m − 9 = 0
Similarly, this quadratic expression would not factorize to yield the required solutions.
Hence, the correct equation is option (A) ( m + 5 ) ( m − 9 ) = 0 .

Answered by MasonWilliamTurner | 2025-07-06