#### Solution

Let $f (x) = x^4 + a_1x^3 + a_2x^2 + a_3x + a_4$. By hypothesis, $f (x_0) = f ‘(x_0) = 0$. Consequently, $x_0$ is the double root of the polynomial $f (x)$, that is, the polynomial $f (x)$ is divisible by $(x – x_0)^2$.

#### Answer

See the solution above.