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# Roots of Polynomials

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912
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What are the roots of the polynomial \(x^3-12x^2+44x-48=0\)?

I know the method of first using the Rational Roots Theorem and then using long division. In this case, 48 has 10 factors and testing out all of them plus their negatives seems like a lot of work. Is there a quicker way?

Jun 18, 2020

#1
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Hint: Before trying to use the rational root theorem, try to test some values of x and find a pattern in their behavior.

Test values from -4 to 4 and see how the polynomial reacts. If one of the values makes the equation equal to zero, you can synthetic division to continue on with the process.

Jun 18, 2020
#2
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Why specifically the values from -4 to 4? Thanks!

thelizzybeth  Jun 18, 2020
#3
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Sorry for not being clear. Basically, you would want to test all the values around zero,

tertre  Jun 18, 2020
edited by tertre  Jun 18, 2020
edited by tertre  Jun 18, 2020
#4
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Oh ok, I see. Thanks for helping out :)

thelizzybeth  Jun 18, 2020