Question

Consider the line ax + by + c = 0 and the quadratic equation ax2+ cx + b = 0. If the roots of quadratic equation are equal, then
the area of the triangle formed by the line with the co-ordinate
axis is
(1) 1
(2) 2
(3) 4
(4) 1/2​

Answer 1

For the quadratic equation ax2+bx+c=0,a,b,c,εQ

Roots are given by 

α=2a−b+b2−4ac and 

β=2a−b−b2−4ac

If D=0 then α=2a−b=β i.e. the roots are equal and real. 

Since a,b and c∈Q, the roots will be equal and rational.