anonymous
  • anonymous
What are the roots of the polynomial equation x^4+x^3=4x^2+4x? –2, –1, 0, 2 –2, 0, 1, 2 –1, 0 0, 1
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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freckles
  • freckles
you could write everything on one side and try to factor
welshfella
  • welshfella
x^4+x^3=4x^2+4x x^4 + x^3 - 4x^2 - 4x = 0 take out the common factor x x(x^3 + x^2 - 4x - 4) = 0 so what is one root?
welshfella
  • welshfella
when two expression are multiplied and the result is zero then either one = zero right?

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anonymous
  • anonymous
yes, so it would be D?
welshfella
  • welshfella
dont jump to conclusions all we can say is that x = 0 one root is 0
welshfella
  • welshfella
- so it could be any of the 4 options now we can look to see if we can factor the cubic in the parentheses
welshfella
  • welshfella
x^3 + x^2 - 4x - 4 = 0
welshfella
  • welshfella
we can factor this by grouping can you factor the first 2 terms x ^3 and x^2 - what is the highest common factor of these 2?
welshfella
  • welshfella
what is the highest thing which divides into x^3 and x^2?
welshfella
  • welshfella
is it x or is it x^2?
anonymous
  • anonymous
it would be x^2
welshfella
  • welshfella
yes so it factors to x^2(x + 1) OK with that?
anonymous
  • anonymous
yes
welshfella
  • welshfella
right so so far we have x^1(x + 1) - 4x - 4 = 0 it would be nice if we could get another (x + 1) so we could factor further and we can do this by taking out -4 from the lat 2 terms so we get x^2( x + 1) - 4(x + 1) = 0 taking out the x+ 1 (x^2 - 4)(x + 1) = 0 do you follow that ok?
anonymous
  • anonymous
sure do :)
welshfella
  • welshfella
great so now we have x^2 - 4 = 0 and x + 1 = 0 x = 2 , -2 and -1 so final answer is 2, -2, -1 and 0
welshfella
  • welshfella
A is correct
anonymous
  • anonymous
Thank you for explaining this to me!!!
welshfella
  • welshfella
yw
welshfella
  • welshfella
its always worth checking to see if you can factor by grouping
welshfella
  • welshfella
you cant always do it of course

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