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

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

Question 885534: What are the zeroes of f(x) = x^3 + 5x^2 - 7x + 1?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
f(x) = x^3 + 5x^2 - 7x + 1
p = factors of the constant term.
q = factors of the leading term.
possible rational solutions are factors of p divided by factors of q.
this would make them +/- 1.
use synthetic division to see if either one of these is a rational root.
1 is a root which means that (x-1) is a factor.
the remainder of the synthetic division is x^2 + 6x - 1
the roots of this equation are x = -3 + sqrt(10) and -3 - sqrt(10)
this equation has 1 real rational root and 2 real irrational roots.
the real rational root is x = 1
the real irrational roots are -3 +/- sqrt(10)
a graph of your equation is shown below:
the dashed vertical lines show you where the roots are.
they are at x = 1, x = -3 - sqrt(10) and x = -3 + sqrt(10)
-3 - sqrt(10) is roughly equal to x = -6.16.
-3 + sqrt(10) is roughly equal to x = 0.16.
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