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Polynomial and Its General Form

If -1 is a ...

Question

If $- 1$ is a zero of polynomial $p (x) = a x^{2} + x^{2} + x + 4$ find the value of $- a$

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Solution

$p (x) = a x^{2} + x^{2} + x + 4$

$p (- 1) = a {(- 1)}^{2} + {(- 1)}^{2} + (- 1) + 4$

$0 = a + 1 - 1 + 4$

$a = - 4$

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