Question

If `m_(1),m_(2)` be the roots of the equation `x^(2)+(sqrt(3)+2)x+sqrt(3)-1 =0`, then the area of the triangle formed by the lines `y = m_(1)x,y = m_(2)x` and `y = 2` is
A. `sqrt(33)-sqrt(11)` sq. units
B. `sqrt(11) +sqrt(33)` sq. units
C. `2sqrt(33)` sq. units
D. 121 sq. units

Answer 1

Correct Answer - B
Sides are along lines `y = m_(1)x,y = m_(2)x` and `y = 2`
`:.` Vartices of the triangle are `(0,0), ((2)/(m_(1)),2),((2)/(m_(2)),2)`
Area `=(1)/(2) |quad{:(0,0),((2)/(m_(1)),2),((2)/(m_(2)),2),(0,0):}|`
` =2|(m_(2)-m_(1))/(m_(1)m_(2))|`
`:. |m_(1)-m_(2)| =sqrt((m_(1)+m_(2))^(2)-4m_(1)m_(2))`
`= sqrt((sqrt(3)+2)^(2)-4(sqrt(3)-1))`
`= sqrt(11)`
`:.` Area `= 2|(sqrt(11))/(sqrt(3)-1)| =sqrt(33)+sqrt(11)`