Through the point (1, 1), a straight line is drawn so as to form with coordinate axes a triangle of area S. The intercepts made by the line on the coordinate axes are the roots of the equation

If a, b are the intercepts made by the line, then the equation of the line is xa+yb=1Since it passes through (1, 1), ∴   1a+1b=1⇒a+bab=1       ----(1)Also, area of the triangle made by the straight line on the coordinate axes is S∴12ab=S i,e., ab=2S  -----(2)So, by (1),  a+b=2S  -----(3)From (2) and (3), the intercepts a and b are the roots of the equation x2-2Sx+2S=0.