If m₁ and m₂ are the roots of the equation x^2+( 3 +2) x+( 3 -1)=0, then the area of the triangle formed by the lines y=m₁ x, y=m₂ x and y=c

Step-by-step solution

Since, m₁ and m₂ are the roots of the equation x^2+( 3 +2) x+( 3 -1)=0 then m₁+m₂=-( 3 +2) , m₁ m₂= 3 -1 m₁-m₂= (m₁+m₂ )^2-4 m₁ m₂ = (3+4+4 3 -4 3 +4) = 11 and coordinates of the vertices of the given triangles are (0,0), (c / m₁, c ) and (c / m₂, c ) . Hence, the required area of triangle = 1 2 | array ccc 0 & 0 & 1 c m₁ & c & 1 c m₂ & c & 1 array |= 1 2 c^2 | ( 1 m₁ - 1 m₂ ) |= 1 2 c^2 |m₂-m₁ | m₁ m₂ = 1 2 c^2 11 ( 3 -1) = 1 2 c^2 11 ( 3 +1) ( 3 -1)( 3 +1) = ( 33 + 11 4 ) c^2