Question : If $(x-2)$ is a factor of $x^2+3Qx – 2Q$, then the value of $Q$ is:
Option 1: 2
Option 2: –2
Option 3: 1
Option 4: –1
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Correct Answer: –1
Solution :
Given: $(x-2)$ is a factor of $x^2+3Qx-2Q$.
Since $(x-2)$ is a factor of $P(x)=x^2+3Qx-2Q$.
Then, $P(2)=0$
So, $x^2+3Qx-2Q=0$
$⇒2^2+3Q\times2-2Q=0$
$⇒4+6Q-2Q=0$
$⇒4Q=-4$
$\therefore Q=-1$
Hence, the correct answer is –1.
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