Question

How do you write a polynomial in standard form given the zeros x=1, -1, √3i, -√3i?

Answer 1

When we know the zeros of a polynomial `z_i` , we can obtain the polynomial, by multiplying a constant different of zero, `a`, by the product of all `(x-z_i)`.

If zeros are `1, -1, sqrt(3)i, -sqrt(3)i`

The polynomial will be:

`a(x-1)(x+1)(x-sqrt(3)i)(x+sqrt(3)i)`

`a(x^2-1)(x^2+3)`

`a(x^4+3x^2-x^2-3)`

`a(x^4+2x^2-3)`, where a is any real number except zero.