DarkBlueChocobo
  • DarkBlueChocobo
Help with polynomials
Mathematics
chestercat
  • chestercat
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DarkBlueChocobo
  • DarkBlueChocobo
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DarkBlueChocobo
  • DarkBlueChocobo
DarkBlueChocobo
  • DarkBlueChocobo
I don't understand how to find it :/

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Sepeario
  • Sepeario
I think you expand it and then use discriminant?
DarkBlueChocobo
  • DarkBlueChocobo
Can you explain the discriminant
phi
  • phi
the "roots" of a polynomial are the x values that make the polynomial zero. here you have \[ (x-4)^2 (x^2+4) = 0\] or \[ (x-4) (x-4) (x^2+4) = 0\] as you can see, if x= 4 (twice, so it is a repeated root) you get zero you would also get 0 if x^2+4=0 or \( x^2= -4 \) take the square root of both sides and you get \[ x= 2i \text{ or } x=-2i\] the 4 roots are: 4,4,+2i, -2i
phi
  • phi
Statement I is true: you have two imaginary roots: 2i and -2i II is false: you do have the real root 4 III is true: you have four complex roots, namely 4,4, 2i and -2i statement III is a bit tricky, because we must recognize that pure real (like 4) and pure imaginary (like 2i) can both be categorized as complex.
ali2x2
  • ali2x2
I and III are true.

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