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prove that 2b=a+c, if (b-c) x^2 …

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prove that 2b=a+c, if (b-c) x^2 + (c-a)x + (a-b) =0 has two real and equal roots

    • Posted by Susmita Mandal 7 years, 6 months ago

    CBSE > Class 10 > Mathematics
    • 1 answers

    Devender Mangla 7 years, 6 months ago

    (b-c)x^2+(c-a)x+(a-b) =0 has real roots so D = 0 B^2 - 4ac =0 = (c-a)^2-4*(b-c)*(a-b)=0 = C^2 +a^2-2ac -4* (ab-ac- b^2+bc) = 0 = C^2+a^2-2ac -4ab+4ac +4 b^2 -4 bc = 0 = C^2+a^2+2ac = 4ab - 4b^2 + 4 bc = (a+c)^ 2 = 4b( a - b + c) √[ a+ c] ^ 2 = √ 4b^2 = a+ c = 2 b

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