Question 470258: I need to identify all of the real roots of the polynomial equation x^3+6x^2-5x-30=0 by using the rational root theorem. Will you please help me?
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! I need to identify all of the real roots of the polynomial equation x^3+6x^2-5x-30=0 by using the rational root theorem.
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p(x)=x^3+6x^2-5x-30
factors of p=30:±1,±2,±3,±5,±6,±10,±15,±30
factors of q=±1
Possible rational roots (p/q): ±1,±2,±3,±5,±6,±10,±15,±30
Finding roots by synthetic division
0)......1......6......-5......-30
1)......1......7.......2.......-28
2)......1......8.......11......-8
3)......1......9.......22......36 (3 is upper bound)
-2)....1......4.....-13......-4
-3)....1......3.....-14......12
-6)....1......0......-5........0 (-6 is a root)
p(x)=(x+6)(x^2-5)
x^2-5=0
x=±√5
p(x)=(x+6)(x-√5)(x+√5)
Roots: -6, √5, -√5
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