Question 30

If highest common factor of $$x^{2}-px-q$$ and $$5x^{2}-3px-15q$$ is (x - 3), then value of (p , q) will be :

Solution

$$(x-3)$$ is a factor of $$x^{2}-px-q$$ and $$5x^{2}-3px-15q$$, thus, at x = 3, the value of polynomial will be equal to 0. Therefore,

$$3p+q=9$$ and $$9p+15q=45$$

Solving the above equations, we will get $$p=\dfrac{5}{2}\ and\ q=\dfrac{3}{2}$$

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