Question 327180: find the zeros of the following polynomial f(x)= x^3-4x^2-7x+10
Answer by galactus(183)   (Show Source):
You can put this solution on YOUR website! Per the Rational Root Theorem, we see that 1, 2, 5 are possible roots.
We know this by looking at the constant term, 10. What divisors does 10 have?.
1,2,5,10. We can also check the negative of these as well.
By using division, we can test these roots and see. Try 5. If we divide the given cubic by x-5 and it reduces to a quadratic, we have a root.
Doing so, reults in x^2+x-2
Yep, 5 is a root.
Now, a little ol' quadratic that is easily factorable.
What two numbers when multiplied equal -2 and when added equal 1?.
How about 2 and -1?.
x^2+2x-x-2
x(x+2)-(x+2)
(x-1)(x+2)
So, the factored form of the cubic is (x-5)(x-1)(x+2)
So, it has roots 5,1,-2.
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