If a, b, c are rational and no two of them are equal then the equations (b-c)x^2+(c-a)x+a-b=0 and a(b-c)x^2+b(c-a)x+c(a-b)=0

JEE Advanced Mathematics question

If are rational and no two of them are equal then the equations

(b-+(c-a)x+a-b=0

and

a(b-+b(c-a)x+c(a-b)=0

(A)have rational rootsCorrect
(B)will be such that at least one has rational rootsCorrect
(C)have exactly one root commonCorrect
(D)have at least one root commonCorrect

Answer: (A),(B),(C),(D)

Solution

In each equation the coefficients add up to 0, so is a root of both. - First equation: other root (product of roots), rational. - Second equation: other root , rational. (If it degenerates to , root .)

So: - (a) ✔ bot

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Question ID VK-108021