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Statement-I : If roots of the equation $$x^2- bx + c = 0$$ are two consecutive integers, then $$b^2- 4c = 1$$.
Statement-II : If $$a, b, c$$ are odd integers, then the roots of the equation $$4abcx^2 + (b^2- 4ac)x- b = 0 $$ 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-I
If roots of the equation $$x^2-bx+c=0$$ are two consecutive integers.
$$\Rightarrow$$ Difference between roots is $$1$$.
$$\Rightarrow \displaystyle\frac{\sqrt{\Delta}}{a}=1$$
$$\therefore b^2-4c=1$$
$$4abc x^2+(b^2-4ac)x-b=0$$
$$\Delta = (b^2-4ac)^2+164ab^2c=(b^2+4ac)^2>0$$  ($$\because a,b,c$$ are odd integers.)
$$\therefore$$ Roots are real and distinct.
Statement-I is true, Statement-II is true ; Statement-II is NOT a correct explanation for statement-I
Hence, option B.

Mathematics

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