anonymous
  • anonymous
find a quadratic equation with the roots -1+4i and -1-4i
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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jango_IN_DTOWN
  • jango_IN_DTOWN
quadratic equation with roots x=a and x=b are given by (x-a)(x-b)=0
jango_IN_DTOWN
  • jango_IN_DTOWN
so we have (x-(-1+4i))(x-(-1-4i))=0
jango_IN_DTOWN
  • jango_IN_DTOWN
implies (x+1-4i)(x+1+4i)=0 implies (x+1)^2+16=0

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jango_IN_DTOWN
  • jango_IN_DTOWN
implies x^2+2x+17=0
jango_IN_DTOWN
  • jango_IN_DTOWN
@Hope214
anonymous
  • anonymous
i dont understand can you please explain?
jango_IN_DTOWN
  • jango_IN_DTOWN
ok.. see if the roots are a and b, the equation is given by (x-a)(x-b)=0
jango_IN_DTOWN
  • jango_IN_DTOWN
here a=-1+4i and b=-1-4i so plug them in the equation (x-a)(x-b)=0
anonymous
  • anonymous
ok so once you plug them in what do you do
jango_IN_DTOWN
  • jango_IN_DTOWN
then we reduce it in the general quadratic form which is px^2+qx+r=0 where p,q,r are constants
jango_IN_DTOWN
  • jango_IN_DTOWN
now lets get back to the problem, after substitutiong we have (x-(-1+4i))(x-(-1-4i))=0 implies (x+1-4i)(x+1+4i)=0
jango_IN_DTOWN
  • jango_IN_DTOWN
implies {(x+1)-4i}{(x+1)+4i}=0 now use the formula (a-b)(a+b)=a^2-b^2 and you get (x+1)^2-(4i)^2=0 implies (x+1)^2+16=0
jango_IN_DTOWN
  • jango_IN_DTOWN
implies x^2+2x+1+16=0 implies x^2+2x+17=0
anonymous
  • anonymous
ok thank u

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