Question 38

If the expression $$px^3 - 2x^2 - qx + 18$$ is completely divisible by $$(x^2 - 9)$$, then what is the ratio between p and q respectively?

Solution

Expression : $$f(x)=px^3 - 2x^2 - qx + 18$$ is divisible by $$(x^2 - 9)$$

=> $$x^2-9=0$$

=> $$x^2=9$$

=> $$x=\sqrt9=3$$

Thus, $$f(3)=0$$

=> $$p(3)^3-2(3)^2-q(3)+18=0$$

=> $$27p-18-3q+18=0$$

=> $$27p=3q$$

=> $$\frac{p}{q}=\frac{3}{27}=\frac{1}{9}$$

=> Ans - (A)

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