SOLUTION: What are the zeroes of f(x) = x^3 + 5x^2 - 7x + 1?

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Question 885552: What are the zeroes of f(x) = x^3 + 5x^2 - 7x + 1?
Answer by nerdybill(7384)   (Show Source): You can put this solution on YOUR website!
f(x) = x^3 + 5x^2 - 7x + 1
possible zeros are -1 and 1.
use synthetic division to check
1 | 1 5 -7 1
1 6 -1
-----------------
1 6 -1 0
since the remainder is zero it is a factor:
(x-1)(x^2+6x-1)
normally, you would factor the quadratic but since it can't be factored we use the "quadratic formula" to get
zeroes are at:
x = 1; x = 0.1623; and x = -6.1623
.
details of quadratic equation follows:
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=40 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 0.16227766016838, -6.16227766016838. Here's your graph:
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