Question 1147243: -3x^4-7x+17=0 how many complex roots does this polynomial equation have?
Found 2 solutions by Boreal, rothauserc:
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! this has one sign change with original function, so it has one positive root.
with -x for x
-3x^4+7x+17=0
this also has one sign change, so there is one negative root. That leaves two other roots in this fourth power function and they are conjugate complex roots.
Two.
Answer by rothauserc(4718)  (Show Source):
You can put this solution on YOUR website! -3x^4 -7x +17 = 0
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The Fundamental Theorem of Algebra says that this equation will have 4 roots(this is the degree of the polynomial)
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The Rational Roots Theorem says that if this equation has rational roots, then
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q could be +or - 1, + or - 3
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p could be + or - 1, + or - 17
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x = + or - 1, + or - 17, + or - 1/3, + or - 17/3
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none of these possible roots satisfy the equation, therefore
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we consider the graph of the equation
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Therefore, this equation has 2 complex roots and 2 rational roots
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if we wanted to determine all the roots for x, then we would turn to using Newton's method for finding the rational roots first
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