Question

What are the zeros of the polynomial `f(x) = x^3 + 3x^2 - 7x`?

Answer 1

Zeros of `x^3+3x^2-7x` are `{0,(-3-sqrt37)/2,(-3+sqrt37)/2}`

Explanation:

As `x` is a factor of `x^3+3x^2-7x`, one of the zeros is `0`. Dividing `x^3+3x^2-7x` by `x`, we get `x^2+3x-7`.

As the discriminant `b^2-4ac` in `x^2+3x-7` is `3^2-4×1×(-7)=9+28=37`, which is not perfect square. Hence other two zeros are not rational. These are given by quadratic formula `(-b+-sqrt(b^2-4ac))/(2a)` i.e.

`(-3+-sqrt37)/2`

As such zeros of `x^3+3x^2-7x` are `{0,(-3-sqrt37)/2,(-3+sqrt37)/2}`