IF `alpha,beta` are the roots of the equation `6x^(2)-5x+1=0`, then the value of `tan^(-1)alpha+tan^(2)beta` is

Options

A. `0`
B. `(pi)/(4)`
C. `1`
D. `(pi)/(2)`

Answer

B

Explanation

Let `alpha,beta` are the roots of given equation
`6x^(2)-5x+1=0`
`impliesalpha+beta=(5)/(6) and alphabeta=(1)/(6)`
`thereforetan^(-1)alpha+tan^(-1)beta=tan^(-1)((alpha+beta)/(1-alphabeta))`
`=tan^(-1)(((5)/(6))/(1-(1)/(6)))=tan^(-1)(1)=(pi)/(4)`