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
Text Solution
Verified by Experts
The correct Answer is:
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)`
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CENGAGE-COORDINATE SYSTEM-Multiple Correct Answers Type
