Dark435
Dark435 Dark435
  • 28-07-2018
  • Mathematics
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three of zeroes of a fourth degree polynomial equation are 1,-1,2i. Write the equation for the function if f(0) = 8

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konrad509
konrad509 konrad509
  • 28-07-2018

[tex] a(x-1)(x+1)(x-2i)(x+2i)=\\
a(x^2-1)(x^2+4)=\\
a(x^4+4x^2-x^2-4)=\\
a(x^4+3x^2-4)\\\\
a(0^4+3\cdot0^2-4)=8
a\cdot(-4)=8\\
a=-2\\\\
-2(x^4+3x^2-4)=\boxed{-2x^4-6x^2+8} [/tex]

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