SOLUTION: Find a polynomial P(x) with real coefficients having a degree 6, leading coefficient 3, and zeros 6,0 (multiplicity 3), and 2-4i.

Question 1098636: Find a polynomial P(x) with real coefficients having a degree 6, leading coefficient 3, and zeros 6,0 (multiplicity 3), and 2-4i.

Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

This is quite straightforward if you know the basic principles.

The root of 6 means the polynomial has a factor of (x-6); the root of 0 with multiplicity 3 means the polynomial has a factor of x (i.e., x-0) three times.

And since complex roots have to occur in conjugate pairs if the polynomial has real coefficients, the root of 2-4i means the polynomial has to have factors of (x-(2-4i)) and (x-(2+4i)).

And then there can be a scalar multiplier, a; so the polynomial is

Presumably, if you are working a problem like this, you know how to expand that expression, if the answer is required in standard polynomial form.
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