Question

If $a,b,c,x$ are real numbers and $(a^2+b^2)x^2-2b(a+c)x+(b^2+c^2)=0$ has real & equal roots, then $a,b,c$ are in

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

Answer 1

Answer: (B)

$G.P$

Since $(a^2+b^2)x^2-2b(a+c)x+(b^2+c^2)=0$ has real & equal roots.

$\therefore$ $4b^2(a^2+c^2+2ac)-4(a^2+b^2)(b^2+c^2)=0$

$4b^2{a}^2+4b^2{c}^2+8ac{b}^2-4a^2{b}^2-4a^2{c}^2-4b^2-4b^2{c}^2=0$

$8ac{b}^2-4a^2{c}^2+4b^4=0$

$(2ac-2b^2{)}^2=0$

$ac=b^2$