Question

If (x - 2) is a factor of \(px^2 - x - 6\) then the value of p is

(A) 2

(B) 3

(C) 1

(D) 4

Answer 1

Correct option is (A) 2

\((x - 2)\) is a factor of \(px^{2}-x-6\).

Then,

\( x-2=0\)

\(\therefore x=2\)

\(p(x)=p x^{2}-x-6\)

\(\Rightarrow p(2)^{2}-2-6=0\)

\(4 p-2-6=0\)

\( 4 p-8=0 \)

\(4 p=8\)

\(p=\frac{8}{4}\)

\( \therefore p=2\)