Question

If x = 2 is a common root of both the equations \(2x^2 + 2x + p = 0\) and \(qx^2 + qx + 18 = 0\) then the value of \((q - p)\) is

(A) -4

(B) -3

(C) 9

(D) 4

Answer 1

Correct option is (C) 9

If x = 2 is a common root.

\(2 x^{2}+2 x+p =0\)

\(2(2)^{2}+2(2)+p =0\)

\(8+4+p =0\)

\(12+p =0\)

\(p =-12\)

and

\(q x^{2}+q x+18 =0\)

\(q(2)^{2}+q(2)+18 =0\)

\(4 q+2q+18 =0\)

\(6q+18 =0 \)

\(6 q =-18\)

\(q =\frac{-18}{6}=-3\)

then,

\((q - p) = -3 -(-12)\)

\(= - 3 + 12\)

\(= 9\)