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How do you find a polynomial function with zeroes 2, -4, -3i?

1 Answer

Oct 23, 2015

$x^{3} + (2 + 3 i) x + (- 8 + 6 i) x - 24 i$ $x^3+(2+3i)x+(-8+6i)x-24i$

Explanation:

If the three roots are given, then we may obtain the corresponding 3 factors and hence write the polynomial as

$(x - 2) (x + 4) (x + 3 i) = 0$ $(x-2)(x+4)(x+3i)=0$

Multiplying this out you will get the polynomial with complex coefficients in standard form

$x^{3} + (2 + 3 i) x + (- 8 + 6 i) x - 24 i$ $x^3+(2+3i)x+(-8+6i)x-24i$

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