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If the polynomial p(x)=x 5 +ax 4 +bx 3 +cx 2 +dx+e has five different intercepts. One of which is(0,0). Then find which of the coefficient cannot be 0.

 If the polynomial p(x)=x5+ax4+bx3+cx2+dx+e has five different intercepts. One of which is(0,0). Then find which of the coefficient cannot be 0.

Grade:9

1 Answers

Arun
25750 Points
4 years ago
Clearly, since $(0,0)$ is an intercept, $e$ must be $0$. But if $d$ was $0$, $x^2$ would divide the polynomial, which means it would have a double root at $0$, which is impossible, since all five roots are distinct.
hence d can't be zero

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