# SOLUTION: this is for college algebra: find a polynomial of lowest degree that has real coefficients, a leading coefficient of 1, and with 5-2i and 3 as two of its zeros

Algebra ->  Algebra  -> Rational-functions -> SOLUTION: this is for college algebra: find a polynomial of lowest degree that has real coefficients, a leading coefficient of 1, and with 5-2i and 3 as two of its zeros      Log On

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 Click here to see ALL problems on Rational-functions Question 62290: this is for college algebra: find a polynomial of lowest degree that has real coefficients, a leading coefficient of 1, and with 5-2i and 3 as two of its zerosAnswer by stanbon(57307)   (Show Source): You can put this solution on YOUR website!find a polynomial of lowest degree that has real coefficients, a leading coefficient of 1, and with 5-2i and 3 as two of its zeroes. -------- If 5-2i is a zero and it has real coefficients then 5+2i is also a zero. So f(x)=(x-3)(x-(5-2i))(x-(5+2i)) f(x)= (x-3)((x-5)^2+4) f(x)= (x-3)(x^2-10x+29) f(x)=x^3-10x^2-3x^2+29x-30x-12 f(x)=x^3-13x^2-x-12 Cheers, stan H.