IF (x-k) IS THE HCF OF x²+x-12 AND 2x²-kx-9 THEN WHAT IS THE VALUE OF p?

if (x-k) is the HCF of the given polynomials therefore (x-k) is the factor of both the polynomials.
since (x-k) is the factor of $x^2+x-12$.
therefore
$$\begin{gathered} k^2+k-12=0 \\ {k}^2+4k-3k-12=0 \\ k(k+4)-3(k+4)=0 \\ (k+4)(k-3)=0 \\ \Rightarrow k=-4 or k=3 \end{gathered}$$
sicne (x-k) is the factor of $2x^2-kx-9$
therefore
$$\begin{gathered} 2k^2-k.k-9=0 \\ 2k^2-k^2-9=0 \\ {k}^2=9 \\ \Rightarrow k=\pm 3 \end{gathered}$$
for k =3 , (x-k) is the factor of both the polynomials.
thus k =3 

hope this helps you