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alvarotrevino11
Answered

A degree 4 polynomial P(x) with integer coefficients has zeros 5 i and 3, with 3 being a zero of multiplicity 2. Moreover, the coefficient of x^4 is 1. Find the polynomial.

Verified Answer :

apologiabiology

Multiplicity
is how many times the root repeats


roots
r1 and r2 of a polynomial factor to


(x-r1)(x-r2)


so 3
multiplicty 2 means (x-3)^2 is in the factorization of that
polynomial




also,
for a polynomial with real coefients, if a+bi is a roots, a-bi is
also a root


5i is
a root, therefor -5i is a root as well




roots
are


(x-5i)(x+5i)(x-3)^2


if we
expand


x^4-6x^3+34x^2-150x+225


the
polynomial is


f(x)=x^4-6x^3+34x^2-150x+225



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