Question 1098636
<br>This is quite straightforward if you know the basic principles.<br>
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.<br>
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)).<br>
And then there can be a scalar multiplier, a; so the polynomial is<br>
{{{P(x) = a(x^3)(x-6)(x-(2-4i))(x-(2+4i))}}}<br>
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.