Find a polynomial function with real coefficients that has the given zeros.1, 5i

Adeline Mooney

Adeline Mooney

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2022-08-18

Find a polynomial function with real coefficients that has the given zeros.1, 5i

Answer & Explanation

helsedel1v

helsedel1v

Beginner2022-08-19Added 11 answers

Since 1 and 5i are zeros, the function will have (x-1) and (x-5i) as factors. Complex zeros come in conjugate pairs so (x+5i) is also a factor.
The polynomial function can be written as f(x)=a(x-1)(x-5i)(x+5i), where aR.
Let us substitute 1 for a and multiply to get one of the functions:
f(x)=(x-1)(x-5i)(x+5i)
=(x1)(x25ix+5ix25i2)
=(x1)(x2+25)
Let us multiply terms in the last two pairs of parentheses:
=x3+25xx225
=x3x2+25x25
Result:
x3x2+25x25

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