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If a ,b ,c in R such that a+b+c=0a n da...

If `a ,b ,c in R` such that `a+b+c=0a n da!=c` , then prove that the roots of `(b+c-a)x^2+(c+a-b)x+(a+b-c)=0` are real and distinct.

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To prove that the roots of the quadratic equation \((b+c-a)x^2 + (c+a-b)x + (a+b-c) = 0\) are real and distinct given that \(a + b + c = 0\) and \(a \neq c\), we will follow these steps: ### Step 1: Identify the coefficients The coefficients of the quadratic equation are: - \(A = b + c - a\) - \(B = c + a - b\) - \(C = a + b - c\) ...
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