The quadratic equation whose roots are the x and yintercepts of the line passing through (1,1) and making a triangle of area A with the co-ordinate axes is

Step-by-step solution

Equation of the line making intercepts a and b on the axes is x a + y b =1 Since, it passes through (1,1) 1 a + 1 ~b =1 Also the area of the triangle formed by the line and the axes is A . 1 2 ab = A ab =2 ~A From eqs. (i) and (ii), we get, a+b=2 A Hence, a and b are the roots of the eq. x²-(a+b) x+a b=0 x²-2 A x+2 A=0