If m1 and m2 are the roots of the equation x2+(√3 + 2)x+√3-1=0 , then the area (in sq. units) of the triangle bounded by the lines y=m1x,y=m2x and y=2 is

Question

If m1 and m2 are the roots of the equation x2+(√3 + 2)x+√3-1=0 , then the area (in sq. units) of the triangle bounded by the lines y=m1x,y=m2x and y=2 is (A) √33+√11 (B) √33-√11 (C) 2√33 (D) 2√11

Tardigrade Admin · Accepted Answer

Vertices of the triangle formed by the lines y=m1x,y=m2x &y=2 are (0,0),((2/m1) , 2) & ((2/m2) , 2) Area of the triangle =| (1/2) | 0 0 1 (2/m1) 2 1 (2/m2) 2 1 | | =2|(m2 - m1/m1 m2)|=2|((√D/|a|)/(c)a)|=2|(√D/c)|=2|(√b2 - 4 a c/c)| =2(√7 + 4 √3 - 4 (√3 - 1)/√3 - 1)=(2 √11/√3 - 1) =√33+√11 sq. units

Q. If $m_{1}$ and $m_{2}$ are the roots of the equation $x^{2} + (3 + 2) x + 3 - 1 = 0$ , then the area (in sq. units) of the triangle bounded by the lines $y = m_{1} x, y = m_{2} x$ and $y = 2$ is

$33 + 11$

$33 - 11$

$233$

$211$

Q. If m1​ and m2​ are the roots of the equation x2+(3​+2)x+3​−1=0 , then the area (in sq. units) of the triangle bounded by the lines y=m1​x,y=m2​x and y=2 is

33​+11​

33​−11​

233​

211​

Q. If $m_{1}$ and $m_{2}$ are the roots of the equation $x^{2} + (3 + 2) x + 3 - 1 = 0$ , then the area (in sq. units) of the triangle bounded by the lines $y = m_{1} x, y = m_{2} x$ and $y = 2$ is

$33 + 11$

$33 - 11$

$233$

$211$