Question 1146986: Find all solutions of the equation. (Enter all answers including repetitions. Enter your answers as a comma-separated list.)
x^3 − 8x^2 − 19x − 10 = 0
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! The Fundamental Theorem of Algebra tells us that there are 3 solutions to this equation because it is a polynomial of degree 3
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The Rational Roots Theorem tells us that if there are rational roots, then they are + or - 1, + or - 2, + or - 5, + or - 10
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substituting these values into the equation, we find that
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-1 and 10 are rational root solutions to this equation and
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(x+1)*(x-10) = x^2 -9x -10, divide the original equation by this equation and we get x+1, therefore
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(x+1)^2 * (x-10) = x^3 − 8x^2 − 19x − 10, the original equation
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therefore the equation has a double root and the roots are
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-1, -1, 10
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