The function f(x) = x^2+mx+n
m and n are roots of the function
what is the product of m and n?
I'm stumped on this one. Any help?
Hello, steward0099!
Given:
and are roots of the function.
What is the product of and ?
There is a theorem which says: the product of the roots is the contant term,
You can use Algebra to answer the question.
Use the Quadratic Formula to find the two roots: .
The two roots are: .
Now multiply them . . .
Also, if m and n are roots of (Strictly speaking, an equation has "roots". You are looking for the zeros of the function.) then . So, as Soroban said, the product mn is -n. Of course, mn= -n is the same as mn+ n= n(m+n)= 0.
Either m= 0 or m= -n. We also have m= -(m+n) so that m= -m- n which yields n= -2m. So if n is not 0, we must have -n= 2m= m which says that m must be 0. That is, either m= 0 or n= 0. In either case mn= 0.