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

Question and options

If highest common factor of

x^{2}-p x-q

and

5 x^{2}-3 p x-15 q

(x-3)

, then value of (

\left.p, q\right)

will be :

Correct answer: C - $\left(\frac{5}{2}, \frac{3}{2}\right)$

x=3 is a root of both: 9-3p-q = 0 and 45-9p-15q = 0, i.e. 3p+q = 9 and 3p+5q = 15. Then 4q = 6, so q = 3/2 and p = 5/2.