Question

If the roots of the equation a ( b - c ) x2 + b ( c - a )x + c( a - b ) = 0 are equal, then a, b, c are in 
a) A.P
b) G.P
c) H.P

Answer 1

as roots are equal discriminant is zero
b²(c-a)²=4ac(b-c)(a-b)
c²b²+a²b²-2acb²=4ac(ab-b²-a+bc)=4a²bc-4ab²c-4a²c+4abc²
solve it 
then u will find that
$\frac{2}{b}= \frac{1}{a}+ \frac{1}{c}$