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College Algebra

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how do I find a 4th degree polynomial that has zeros; i,3i with f(-1)=60

I know the conjucants are -i and -3i

(x-i)(x-3i) (x+i)(x=3i)

  • College Algebra - ,

    So, multiply it out to get

    f(x) = a(x^2+1)(x^2+9) = a(x^4+10x^2+9)

    Now, f(-1) = a(1+10+9) = 20a, so we need a=3 and thus

    f(x) = 3(x^4+10x^2+9)

    BTW, that's "conjugates"

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