The graph of the polynomial $P(x)=x^5+a x^4+b x^3+c x^2+d x+e$ has five distinct intercepts, one of

Question

The graph of the polynomial $P(x)=x^5+a x^4+b x^3+c x^2+d x+e$ has five distinct intercepts, one of which is at $(0,0)$. Then the coefficient that cannot be zero is

Professor PC Thomas Classes · Answer

An origin root sets $e=0$. Four distinct remaining roots guarantee a non-zero product, establishing $d 
eq 0$.