To find an equation that has solutions of m = 5 and m = 9, we can use the concept of factoring a quadratic equation based on its roots. If m = 5 and m = 9 are the solutions, we can represent the equation in factored form as follows:
(m – 5)(m – 9) = 0
Next, we can expand this expression to obtain the standard form of the quadratic equation:
m² – 9m – 5m + 45 = 0
This simplifies to:
m² – 14m + 45 = 0
Therefore, the equation that has the solutions m = 5 and m = 9 is:
m² – 14m + 45 = 0