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?
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)