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Question

If a, b, c are rational and ab, ba+c, then the roots of the equation (a+cb)x2+2cx+(b+ca)=0 are

A
irrational and distinct
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B
distinct integers
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C
rational and distinct
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D
rational and equal
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Solution

The correct option is C rational and distinct
D=(2c)24(a+cb)(b+ca)
D=4c24(c+(ab))(c(ab))
=4c24(c2(ab)2)
D=4(ab)2
D>0(ab) and is a perfect square.
So, roots are rational and distinct.

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