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24 February, 14:27

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

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  1. 24 February, 14:45
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    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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