Question

If roots of the equations $(b-c)x^2+(c-a)x+a-b=0$, where $b\ne c$, are equal, then a, b, c are in?

• A. G.P.
• B. H.P.
• C. A.P.
• D. A.G.P.

Answer 1

The correct option is C A.P.

$(b-c)x^2+(c-a)x+a-b=0$

Root are equal, so $D=0$

$\Rightarrow (c-a{)}^2-4(b-c\left)\right(a-b)=0$

$\Rightarrow c^2+a^2-2ac-4ab+4b^2+4ac-4bc=0$

$\Rightarrow c^2+a^2+4b^2+2ac-4ab-4bc=0$

$\Rightarrow (a+c-2b{)}^2=0$

$a+c=2b$