SOLUTION: find the real roots of the polynomial y=3x^4-5x^3-5x^2+5x+2

Question 558200: find the real roots of the polynomial y=3x^4-5x^3-5x^2+5x+2
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
find the real roots of the polynomial y=3x^4-5x^3-5x^2+5x+2
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The coefficients add up to 0 so x = 1 is a root.
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Use synthetic division to find the other roots:
1)....3....-5....-5....5....2
.......3.....-2....-7...-2...|..0
Quotient: 3x^3 - 2x^2 -7x -2
x = -1 is a root
-1)....3....-2....-7....-2
........3.....-5....-2...|..0
Quotient: 3x^2-5x-2
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Find the roots of the quadratic:
x = [5 +- sqrt(25-4*-2)]/6
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x = [-5 +- sqrt(33)]/6
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You now have the 4 roots
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Cheers,
Stan H.
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