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11 August, 12:36

Write a polynomial function with rational coefficients so that p (x) = 0 has the given roots: - 5 and 3i

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  1. 11 August, 13:09
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    For a polynomial with ratinal coefients, if a+bi is a root, then a-bi is a root

    since 0+3i is a root, 0-3i is also a root

    if the roots of an equtation are r1, r2, r3, the factored form of the polynomial is like this

    (x-r1) (x-r2) (x-r3)

    given

    roots are - 5, 3i and - 3i

    (x - (-5)) (x-3i) (x - (-3i)) or

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

    if we expand

    x³+5x²+9x+45
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