Question 873059
Q:
Write the simplest third degree polynomial with integer coefficient that has -2 and square root 5 as zeros
A:
If {{{sqrt(5)}}} is a root , then the conjugate {{{-sqrt(5)}}} is also a root since the coefficients of the polynomial are integers.
{{{sqrt(5)}}} and {{{-sqrt(5)}}} are roots of the quadratic equation {{{x^2 - 5 = 0}}}. Therefore, the third degree polynomial is {{{(x + 2)(x^2 - 5) = 0}}} or {{{highlight(x^3  + 2x^2 - 5x - 10 = 0)}}}.
The polynomial function is {{{highlight(f(x) = x^3  + 2x^2 - 5x - 10)}}}