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

Degree: 4; zeros: 4i and 5i Form a polynomial, f(x), with real coefficients having the given degree and zeros.

Degree: 4; zeros: 4i and 5i

Verified Answer :

MissPhiladelphia

The question indicates that 4i and 5i are imaginary so, they cannot have real roots.

f(x) = (x - 4i)(x + 4i)(x - 5i)(x + 5i)
Then simplify it and it would look like this,

(x^2 + 16)(x^2 + 25)

Simply it again.
x^4 + 16x^2 + 25x^2 + 400
x^4 + 41x^2 + 400

The polynomial that is required is 
f(x) = x^4 + 41x^2 + 400

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