SOLUTION: What are the zeros of p(x)=x^4+7x^3+9x^2-17x-20 solved algebraically?

Question 250698: What are the zeros of p(x)=x^4+7x^3+9x^2-17x-20 solved algebraically?
Answer by drk(1908) (Show Source): You can put this solution on YOUR website!
We are given this polynomial:
p(x) = x^4 + 7x^3 + 9x^2 - 17x - 20.
Using PNI, we get
P . . . N . . . I
1 . . . 3 . . . 0
1 . . . 1 . . . 2.
So, I know there MUST be 1 positive root.
Now I look at P/Q; all the factors of 20 over all the factors of 1.
+-20 +-10 +-5 +-4 +-2 +-1.
I use synthetic division until I find a hit: (X + 4) and (X + 1) are factors of P(x).
So, (X + 4)(X + 1)[X^2 + 2X - 5] = P(x).
The zero's become
X = -4, -1, -1 + sqrt(6), -1 - sqrt(6).
RELATED QUESTIONS
Find all zeros of the polynomial: P(x) = x^3 − 7x^2 + 17x − 15 (answered by jsmallt9)

what are the positive zeros of... (answered by Alan3354,KMST)

what are the real zeros for... (answered by Fombitz)

what are the zeros for... (answered by RAY100)

State the number of positive real zeros, negative real zeros, and imaginary zeros for... (answered by Nate)

state the number of positive real zeros, negative real zeros, and imaginary zeros for... (answered by richwmiller)

Given the polynomial function f(x),find the rational zeros,then the other zeros(that... (answered by lwsshak3)

5x^3-9x^2-17x-3 i have to solve this as follows: (a) By using the Rational Zero... (answered by stanbon)

Write the equation p(x)=2x^4+9x^3+17x^2+19x-15 in factored form... (answered by stanbon)