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If the roots of the equation (b-c)x^2 + (c-a)x + (a-b)=0 are equal,then prove that 2b=a+c

Asked by 29th January 2014, 5:02 PM
Answered by Expert
Answer:
For equal roots, discriminant should be 0. So, (c-a) - 4(b-c)(a-b)= 0 c - 2ac + a - 4ab + 4b + 4ac - 4bc = 0 c + 2ac + a + 4b - 4ab - 4bc = 0 (c + a) + 4b - 4b(a + c) = 0 [(a + c) - (2b)] = 0 Hence, 2b = a + c
Answered by Expert 29th January 2014, 5:39 PM
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