JIPMAT 2024 (QA) - 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 ( .p, q) will be : | PYQs + Solutions

JIPMAT 2024

Algebra

Quadratic Equations

Medium

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 :

\left(\frac{5}{3}, 4\right)

\left(\frac{-5}{3},-4\right)

\left(\frac{5}{2}, \frac{3}{2}\right)

\left(4, \frac{-3}{5}\right)

Correct Option: 3

x-3

is a factor of the expressions, then

x-3=0,

x=3

should equate both the expressions 0.

Putting

x=3

in the first equation:

3^2-3p-q=0

3p+q=9

--> Eq. 1

Putting

x=3

in the second equation:

5(3)^2-3(3)p-15q=0

9p+15q=45

=3p+5q=15

--> Eq. 2

Subtract Eq. 1 from Eq. 2

4q=6

=q=\frac{6}{4}=\frac{3}{2}

Put this value of q back in Eq. 1, and we'll get

p=\frac{5}{2}

Hence, Option 3 is the answer.

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