Question

How do you write a polynomial in standard form given zeros 4, sqrt(5) and -sqrt(5)?

Answer 1

`x^3-4x^2-5x+20`

Explanation:

The polynomial with zeros: `4,sqrt5` and `-sqrt5` is

`(x-4)(x-sqrt5)(x+sqrt5)` or

`(x-4)(x^2-5)` (using `(a-b)(a+b)=a^2-b^2`)

= `x(x^2-5)-4(x^2-5)`

= `x^3-5x-4x^2+20`

= `x^3-4x^2-5x+20`