Question

How do you write a polynomial function with minimum degree whose zeroes are -1, 2, 3i?

Answer 1

`x^4-x^3+7x^2-9x-18`

Explanation:

If `3i` is zero of this polynomial, `-3i` is also zero of it. Hence

`P(x)=(x-(-1))(x-2)(x-3i)(x-(-3i))`

=`(x+1)(x-2)(x-3i)(x+3i)`

=`(x^2-x-2)(x^2+9)`

=`x^4-x^3+7x^2-9x-18`