anonymous
  • anonymous
Determine how many, what type, and find the roots for f(x) = x4 + 21x2 − 100.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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Hayleymeyer
  • Hayleymeyer
lets take t=x^2
welshfella
  • welshfella
its degree 4 so how many roots will there be?
anonymous
  • anonymous
4

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More answers

Hayleymeyer
  • Hayleymeyer
so we have the equation t^2 +21t-100 =0
welshfella
  • welshfella
yea
Hayleymeyer
  • Hayleymeyer
Looking at the discriminant we have discriminant = \[\frac{ -21\pm \sqrt{21^2-4(1)(-100)} }{ 2}\]
welshfella
  • welshfella
- which can be factored
welshfella
  • welshfella
no need this can be factored
Hayleymeyer
  • Hayleymeyer
simplifying the discriminant we get - t=4 or t= -25
Hayleymeyer
  • Hayleymeyer
we know that x^2 =t so \[x=\sqrt{t}\]
anonymous
  • anonymous
ok
Hayleymeyer
  • Hayleymeyer
we have 2 values of t :) one is positive and one is negative :) what do u think can we put negative value of t in this function to get x- \[x=\sqrt{t}\]?
anonymous
  • anonymous
idk to be honest
welshfella
  • welshfella
t = 4 gives 2 values for x 2 and - 2
Hayleymeyer
  • Hayleymeyer
ok well can the square of any number be negative ?
welshfella
  • welshfella
now the square roots of -25 are imaginary do you know what they are?
welshfella
  • welshfella
yes - you introduce the operator i which stands for the square root of -1.
anonymous
  • anonymous
5i?
welshfella
  • welshfella
so sqrt -15 = -5i and 5 i
welshfella
  • welshfella
*sqrt -25
welshfella
  • welshfella
and theres your 4 roots 2, -2 , 5i and -5i
Hayleymeyer
  • Hayleymeyer
well \[\sqrt{-25} \] does not exists cause -25 is negative so we r left with t=4 puttin t=4 in the equation \[x=\sqrt{t}\]we get x=2 and x=-2 :)
welshfella
  • welshfella
probably you haven't come to complex and imaginary numbers yet. They are not real numbers but they do exist in math.
anonymous
  • anonymous
i have i know what they are...somewhat
welshfella
  • welshfella
Yes - mathematicians introduced them because some problems could not be solved using real numbers alone.
welshfella
  • welshfella
Hayleymeyer obviously hasn't been taught them yet.

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