Math-college

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Find an​ nth-degree polynomial function with real coefficients satisfying the given conditions.

n=4;
i and 3 i are zero;
f(-2)=65

f(x)=
An expression using x as the variable. Simplify your​ answer.

  • Math-college -

    all irrational and complex zeros come in conjugal pairs,
    so if i is a zero , so is -i
    if 3i is a zero , so is -3i
    so we have f(x) = a(x-i)(x+i)(x-3i)(x+3i)
    f(x) = a(x^2 + 1)(x^2 + 9)
    also f(-2) = 65
    a(4+1)((4+9) = 65
    65a = 65
    a = 1

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

    check:
    http://www.wolframalpha.com/input/?i=solve+x%5E4+%2B+10x%5E2+%2B+9%3D0

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