anonymous
  • anonymous
please help! x^4-x^3-2x-4=0 how do i solve the equation by first finding the rational roots?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
possible roots are +-1, +-2, +-4
anonymous
  • anonymous
then i found the roots -1 and 2 by synthetic division, how do i find the third/fourth root?
anonymous
  • anonymous
factor, you will have a quadratic left, use the quadratic formula

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anonymous
  • anonymous
i have two quadratics left from -1 and 2. which one do i use?
anonymous
  • anonymous
you know what i means by factor? you said -1 is a root, so \[x^4-x^3-2x-4=(x+1)(\text{some cubic})\]
anonymous
  • anonymous
you can find the cubic by synthetic division
anonymous
  • anonymous
then from the cubic expression factor out the other root \(x-2\) so you will have \[x^4-x^3-2x-4=(x+1)(x-2)(\text{some quadratic})\]
anonymous
  • anonymous
perhaps you can factor the quadratic, but you can always set that equal to zero and solve via the quadratic formula
anonymous
  • anonymous
I'll try solving it
anonymous
  • anonymous
It works. Thank you! So this is the method for solving any question like this?
anonymous
  • anonymous
yes
anonymous
  • anonymous
you should have got \(x^2+2\) for the quadratic
anonymous
  • anonymous
my final answer is {-1,2, +-sqrt2i}

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