Find $a$ and $b$ , if $(x + 1)$ and $(x + 2)$ are factors of $x^{3} + 3 x^{2} - 2 a x + b$

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Solution

$(x + 1)$ is a factor of $x^{3} + 3 x^{2} - 2 a x + b$ means by putting $x = - 1$ in the equation it will become 0.
On putting $x = - 1$ we get $- 1 + 3 + 2 a + b = 0$
$2 a + b = - 2$ ...........(1)
Similarly putting $x = - 2$ we get $- 8 + 12 + 4 a + b = 0$
$4 a + b = - 4$ ............(2)
Solving equation (1) and (2) we get $a = - 1, b = 0$

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