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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.

Text Solution

Verified by Experts

Given equation is
`(b + c - a)^(2) + ( c + a - b) x + ( a + b - c) = 0`
or `(-2a)x^(2) + (-2b)x + (-2c) = 0`
or `ax^(2) + bx + c = 0`
`rArr D = b^(2) - 4ac`
`= (-c - a)^(2) - 4ac`
`= (c - a)^(2) gt 0`
Hence, roots are real and distinct
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