SOLUTION: I need help with this question and I have absolutely no clue how to do it. It states: find all the zeros of the function: x^3+3x^2-x+12

Question 90282: I need help with this question and I have absolutely no clue how to do it. It states: find all the zeros of the function: x^3+3x^2-x+12
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
find all the zeros of the function: f(x) = x^3+3x^2-x+12
I graphed it and found a zero at x=-4
----------
Using synthetic division find the following:
-4)....1....3....-1....12
........1....-1....3...|..0
===============
Remainder = 0 because x=-4 is a zero
Quotient is x^2-x+3
--------------
Find the zeroes of x^2-x+3 using the quadratic formula:
x=[1+-sqrt(1-4*1*3)]/2
x=[1+-sqrt(13)]/2
x= (1+sqrt(13))/2 or x=(1-sqrt(13))/2
==================
You now have three zeroes of f(x)
Cheers,
Stan H.
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