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Question

# Statement-I : If roots of the equation x2âˆ’bx+c=0 are two consecutive integers, then b2âˆ’4c=1.Statement-II : If a,b,c are odd integers, then the roots of the equation 4abcx2+(b2âˆ’4ac)xâˆ’b=0 are real and distinct.

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 B Statement-I is true, Statement-II is true ; Statement-II is NOT a correct explanation for statement-IIf roots of the equation x2−bx+c=0 are two consecutive integers.⇒ Difference between roots is 1.⇒√Δa=1∴b2−4c=14abcx2+(b2−4ac)x−b=0Δ=(b2−4ac)2+164ab2c=(b2+4ac)2>0 (∵a,b,c are odd integers.)∴ Roots are real and distinct.Statement-I is true, Statement-II is true ; Statement-II is NOT a correct explanation for statement-IHence, option B.

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