If `tantheta_1,tantheta_2,tantheta_3` are the real roots of the `x^2-(a+1x^2+1)(b-a)x-b=0,w h e r e""theta_1+""theta_2+""theta_3 in (0,pi)` , then `""theta_1+""theta_2+""theta_3` , is equal to `pi//2` b. `pi//4` c. `3pi//4` d. `pi`

Options

A. `pi//2`
B. `pi//4`
C. `3pi//4`
D. `pi`

Answer

2

Explanation

`tan theta_(1) + tan theta_(2) + tan theta_(3) = (a + 1)`
`sum tan theta_(1) tan theta_(2) = (b - a)`
`tan theta_(1) tan theta_(2) tan theta_(3) = b`
`therefore tan (theta_(1) + theta_(2) + theta_(3)) = (sumtan theta_(1) - II tan theta_(1))/(1 - sum tan theta_(1) tan theta_(2))`
`= (a + 1 - b)/(1 - (b - a)) = 1`
`rArr theta_(1) + theta_(2) + theta+(3) = pi/4`