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algebra

form a polynomial f(x) with real coefficients having the given degree and zeros.

Degree 4; zeros:-3 +5i; 2 multiplicity 2

enter the polynomial f(x)=a(?)

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  1. since complex roots come in pairs, you have
    (x-(-3+5i))(x-(-3-5i))(x-2)^2
    ((x+3)+5i)((x+3)-5i)(x-2)^2
    (x^2 + 6x + 34)(x^2 - 4x + 4)
    x^4 + 2x^3 + 14x^2 - 112x + 136

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  2. degree 4
    zeros 3-5i
    -5 multiplicity 2
    enter the polynomial f(x)=a()

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