anonymous
  • anonymous
Find a polynomial equation with integer coefficients that has the given numbers as solutions and the indicated degree 1 - i, 7i; degree 4 a) x^4+2x^3+51x^2-98x-98=0 b) x^4-2x^3+51x^2-98x-98=0 c) x^4-2x^3+51x^2-98x+98=0 d) x^4-2x^3-51x^2-98x-98=0 e) x^4+2x^3+51x^2+98x+98=0
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
What exactly do you need help with? Try replacing x for the given roots 1 - i and 7i in the equations and see which one is a true equality
anonymous
  • anonymous
yeah, I've tried that. I don't know what to do
anonymous
  • anonymous
post your work and maybe I can help you find where you did mistakes

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anonymous
  • anonymous
I don't even have an idea how to do it
KingGeorge
  • KingGeorge
Since you have roots \(1-i\) and \(7i\), you must also have roots \(1+i\) and \(-7i\). This is an important property of the complex numbers you should probably remember for your class. Now we have 4 different roots, so we can just find what \[(x-(1-i))(x-(1+i))(x-7i)(x+7i)\]is equal to, and you should have a degree 4 polynomial with integer coefficients.
KingGeorge
  • KingGeorge
The specific property says that if you have a root \(a+bi\), you must also have a root \(a-bi\) if your polynomial is in the real numbers.
PaxPolaris
  • PaxPolaris
\[\implies \left( x^2-2x+2 \right)\left( x^2+49 \right)=0\]

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