Posted by **Sue** on Sunday, September 12, 2010 at 6:53pm.

Given f(x)=x^3-7x^2+6x+14, what is the

a. sum of its zeros?

b. product of its zeros?

c. sum of the squares of its zeros?

- Algebra II -
**MathMate**, Sunday, September 12, 2010 at 7:18pm
This is a cubic equation, so there are three roots (real/complex).

If a,b,c represent the three zeroes, and if the left-hand-side is factorizable, then it factorizes into:

(x-a)(x-b)(x-c) which expands to

x³-(a+b+c)x²+(ab+bc+ca)x-abc..(1)

The sum and product of the roots can be read off readily from the above equation (1).

Hint for the sum of squares of the roots:

Consider: The sum of squares of the roots represent:

(a+b+c)²

=**(a²+b²+c²)** + 2(ab+bc+ca)

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