If a , b , c denote the sides of a `!ABC` such that the equation `x^(2)+sqrt2x+1=0` and `ax^(2)+bx+c=0` have a common root , then C =

Options

A. `pi/4`
B. `pi/3`
C. `pi/2`
D. none of these

Explanation

To solve the problem, we need to find the value of \( c \) given that the equations \( x^2 + \sqrt{2}x + 1 = 0 \) and \( ax^2 + bx + c = 0 \) have a common root.

### Step-by-Step Solution:

1. **Identify the roots of the first equation**:
The first equation is \( x^2 + \sqrt{2}x + 1 = 0 \). We can find the roots using the quadratic formula:
\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
...