A polynomial $p(x)$ with real coefficients is of degree five. The equation $p(x)=0$ has a complex root $2+i$. The graph $y=p(x)$ has the x-axis as a tangent at $(2,0)$ and intersects the cordinate axes at $(-1,0)$ and $(0,4)$. Find $p(x)$ in factorised form with real coefficients.
Firts I found the roots:
$r_1=2+i$, $r_2=2-i$, $r_3=-1$, $r_4=2$ and $r_5=a$, I was not able to find it ( for some reason the anwser considered $r_5=2$, but I was not able to prove it)
Observation: if we consider the value of $a=2$ then the answer is right. However I cannot show that $a=2$