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

Mar 12, 2016

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 $\left(x - {z}_{i}\right)$.

If zeros are $1 , - 1 , \sqrt{3} i , - \sqrt{3} i$

The polynomial will be:

$a \left(x - 1\right) \left(x + 1\right) \left(x - \sqrt{3} i\right) \left(x + \sqrt{3} i\right)$

$a \left({x}^{2} - 1\right) \left({x}^{2} + 3\right)$

$a \left({x}^{4} + 3 {x}^{2} - {x}^{2} - 3\right)$

$a \left({x}^{4} + 2 {x}^{2} - 3\right)$, where a is any real number except zero.