# Algebra II

posted by .

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 -

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)

## Similar Questions

1. ### Decartes Rule of Signs

Could you explain to me decartes Rule of signs?
2. ### alg 2

given that one of the zeros of the funiction f(x)=x^3-8x^2+11x+20 is -1, find the sum of the other zeros. hwo do i do this?
3. ### College Algebra

OOPS I got the zeros wrong in the last post...please show work. Find a polynomial of the specified degree that has the given zeros Degree 4: zeros -2,0,2,4

Can someone explain the steps to solve this problem?
5. ### algebra

List all possible rational zeros given by the Rational Zeros Theorem (but don't check to see which actually are zeros). (Enter your answers as a comma-separated list.) S(x) = 6x4 − x2 + 6x + 12
6. ### college algebra

use rational zeros theorem to find all the real zeros in the polynomial function. use zeros to factor f over real numbers. f(x)=x^3+10x^2-13x-22 find real zeros of f?
7. ### calculus

use the given zeros to find the remaining zeros of the function h(x)=x^4-9x^3+12x^2+138x-1360 zero:3-5i enter the remaining zeros of f please show work
8. ### Algebra

Use the rational zeros theorem to list the potential reational zeros of the polynomial function. Do not attempt to find the zeros. f(x)=6x^4+9x^3+30x^2+63x+28
9. ### College algebra

Use the rational zeros theorem to find all the real zeros of the polynomial function. Use the zeros to factor f over the real numbers f(x)=9x^4+28x^3+66x^2+196x+21 Find the real zeros of f Use the real zeros to factor f f(x)=
10. ### Math

f(x)=x64-4x^2+k. Find the values of k so thath the zeros of f satisfy the specified charachteristics. a.four real zeros b.two real zeros, each of multiplicity of two c.two real zeros and two complex zeros d.four complez zeros a.I don't …

More Similar Questions