An equation has solutions of m = –5 and m = 9. Which could be the equation?
Mathematics · High School · Mon Jan 18 2021
Answered on
Given the statement:
An equation has solutions of m = –5 and m = 9.
Determine the equation.
Solution:
Based on the given solution, we can rewrite the equation as,
m + 5 = 0
m - 9 = 0
(m + 5)(m - 9)
Now to equate to the original equation, we simply needed to use the Foil method and multiply the two factors.
Multiply the first term of the first equation, to the first and last term of the second equation. Then, multiply the last term of the first equation, to the first and last term of the second equation.
To clearly see how it works, here's a step by step solution.
= (m)(m)
=m^2
First term of the first equation multiplied to the first term of the second equation.
=(m)(-9)
= -9m
First term of the first equation multiplied to the last term of the second equation.
=(m)(5)
=5m
Last term of the first equation multiplied to the first term of the second equation.
=(5)(-9)
= -45
Last term of the first equation multiplied to the fast term of the second equation.
=m^2 -9m + 5m - 45
=m^2 - 4m - 45
Final answer:
=m^2 - 4m - 45