SOLUTION: What are the solutions of x^3+4x^2+x-6=0 ? a. –1, –2, 3 b. –1, 2, –3 c. 1, –2, –3 d. –1, 2, 3 Searched my textbook, wasn't sure how to solve this. It's not the same as

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Question 986887: What are the solutions of x^3+4x^2+x-6=0 ?
a. –1, –2, 3
b. –1, 2, –3
c. 1, –2, –3
d. –1, 2, 3
Searched my textbook, wasn't sure how to solve this. It's not the same as finding the roots, right?
Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!


It is exactly the same thing as finding roots.

Use synthetic division. I'll do plus and minus 1 for you:
  1  |  1   4    1   -6
            1    5    6
     ------------------
        1   5    6    0
The remainder is zero, so  is a factor, so 1 is a root.

 -1  |  1   4    1   -6
           -1   -3    2
     ------------------
        1   3   -2    4
The remainder is not zero, so  is not a factor, so -1 is not a root.

Note that in the division that proved is a factor, the quotient is , a factorable quadratic polynomial for which you should be able to determine the zeros.

John

My calculator said it, I believe it, that settles it

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