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sahilwasan said – Tue, 10 Mar 2009 19:05:02 -0000 ( Link )

If the quadratic equation (a2+b2)x2+2b(a+c)x+(b2+c2)=0 has equal roots, then (A) a, b and c are in A.P. (B) a, b and c are in G.P. (C) a, c and b are in A.P. (D) a, c and b are in G.P.

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  1. sandevil said – Mon, 16 Mar 2009 05:19:26 -0000 ( Link )

    answr is B.. solve the sum using the fact that b^2-4ac=0,i.e. discriminant=0, when the roots are equal… after simplifying you will get the answer…

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  2. Sureshbala said – Thu, 19 Mar 2009 14:36:57 -0000 ( Link )

    Since the roots are equal the discriminant is 0 i.e \sqrt{b^2-4ac}=0

    \Rightarrow b^2 = 4ac
    \Rightarrow 4b^2 (a+c)^2 = 4(a^2+b^2)(b^2+c^2)
    \Rightarrow b^2 a^2 + b^2 c^2 + b^2 2ac = a^2 b^2 + a^2 c^2 + b^4 + b^2 c^2
    \Rightarrow b^2 2ac = a^2 c^2 + b^4
    The above equation will hold if b^2 = ac
    Hence a,b, and c are in G.P
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