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

The equation `x^(2) + sqrt(2)x + 1 = 0` has imaginary roots, which always occur in pairs. So, the two equations have both common roots.
`thereforea/1=b/(sqrt2)=c/1rArra=lamda,b=sqrt2lamda,c=lamda`
`thereforecosC=(a^(2)+b^(2)-c^(2))/(2ab)rArrcosC=(2lamda^(2))/(2sqrt2lamda^(2))=1/(sqrt2)rArrc=(pi)/4`