The value of a such that `x^2-11 x+a=0` and `x^2-14 x+2a=0` may have a common root is (a)`0` (b) `12` (c) `24` (d) `32.`

Explanation

To find the value of \( a \) such that the equations \( x^2 - 11x + a = 0 \) and \( x^2 - 14x + 2a = 0 \) have a common root, we can follow these steps:

### Step 1: Assume a common root
Let \( \alpha \) be the common root of both equations. Then, we can substitute \( \alpha \) into both equations.

### Step 2: Set up the equations
From the first equation:
\[
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