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?

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- Apr 16th 2012, 08:39 PMsteward0099Function question advanced pre-cal
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? - Apr 16th 2012, 09:07 PMSorobanRe: Function question advanced pre-cal
Hello, steward0099!

Quote:

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 . . .

- Apr 16th 2012, 09:13 PMsteward0099Re: Function question advanced pre-cal
Thank you!

- Apr 17th 2012, 10:08 AMHallsofIvyRe: Function question advanced pre-cal
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.