Find the value of $' a'$ if the polynomial $x^{3} - 5 x^{2} + a x - 2$ has $- 1$ as one of its zeroes

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Solution

We can find the value of $' a'$ by replacing $x$ by $- 1$ and equating the expression to zero.

${(- 1)}^{3} - 5 {(- 1)}^{2} + a (- 1) - 2 = 0$
$- 1 - 5 - a - 2 = 0$
$- 8 - a = 0$
$a = - 8$

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