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Question

If $$(x+2)$$ and $$(x+3)$$ are factors of $$x^3+ax+b$$, find the value of 'a' and 'b'.


Solution

Given polynomial is $$p(x) = x^3+ax+b$$
$$x+2$$ is a factor $$\Rightarrow$$ $$-2$$ is a root of the polynomial.
$$\Rightarrow (-2)^3+a(-2)+b=0 \Rightarrow -2a+b=8$$
$$x+3$$ is a factor $$\Rightarrow -3$$  is a root of the polynomial.
$$\Rightarrow (-3)^3+a(-3)+b=0 \Rightarrow -3a+b = 27$$
Solving the above equations, we get $$a=-19,\ b=-30$$

Mathematics

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