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Question

# Assertion :If a+b+c=0 and a,b,c are rational, then the roots of the equation (b+câˆ’a)x2+(c+aâˆ’b)x+(a+bâˆ’c)=0 are rational . Reason: Discriminant of (b+câˆ’a)x2+(c+aâˆ’b)x+(a+bâˆ’c)=0 is a perfect square .

A
Statement-I is true, Statement-II is true ; Statement-II is correct explanation for Statement-I .
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B
Statement-I is true, Statement-II is true ; Statement-II is NOT a correct explanation for statement-I .
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C
Statement-I is true, Statement-II is false .
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D
Statement-I is false, Statement-II is true .
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Solution

## The correct option is A Statement-I is true, Statement-II is true ; Statement-II is correct explanation for Statement-I .Given a+b+c=0 and a,b,c are rational .(b+c−a)x2+(c+a−b)x+(a+b−c)=0Δ=(c+a−b)2−4(b+c−a)(a+b−c)=(−2b)2−4(−2a)(−2c)=4b2−16ac=4(a−c)2=4((a+c)2−4ac)=4(a−c)2i.e Δ is a perfect square .∴ Roots are rational.∴ Roots are −(c+a−b)±√Δ2(b+c−a) which are rational .Statement-I is true, Statement-II is true ; Statement-II is correct explanation for Statement-I .Hence, option A .

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