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evy15
 2 years ago
Find the rational roots of x^4+8x^3+7x^240x60=0
evy15
 2 years ago
Find the rational roots of x^4+8x^3+7x^240x60=0

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LogicalApple
 2 years ago
Best ResponseYou've already chosen the best response.1You can use the rational roots theorem to guess and check the possible roots. You will find that (x + 2) and (x + 6) are factors of this polynomial. The other factor is (x^2  5). Can you obtain the rational roots from here?

evy15
 2 years ago
Best ResponseYou've already chosen the best response.0yes but how did you get those numbers

LogicalApple
 2 years ago
Best ResponseYou've already chosen the best response.1Using the Rational Roots Theorem (http://www.mathwords.com/r/rational_root_theorem.htm) you guess and check the possible values. The possible rational roots are + p/q where p are the factors of 60 and q are the factors of 1. I.e., the possible rational roots are + 1, +2, +4, +5, +6., etc... By guess and check we can try x = 1, x = 1, x = 2, x = 2 and x = 2. We find that x = 2 results in a 0. That means (x + 2) is a factor. Divide the original polynomial by (x + 2) to obtain a simpler polynomial of degree 3 and repeat the same steps to obtain the next factor.

LogicalApple
 2 years ago
Best ResponseYou've already chosen the best response.1I repeated x = 2 twice by accident in the explanation above. Anyway, to show x = 2 results in a 0: (2)^4+8(2)^3+7(2)^240(2)60 = 16  64 + 28 + 80  60 = 0 So if x = 2, that means (x + 2) must be a factor of the original polynomial. Division yields (see attached file). Our new polynomial is x^3 + 6x^2  5x  30. We can use the same Rational Roots Theorem to determine the remaining possible rational root(s).
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