Multiple choice

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.

  1. Statement-I is true, Statement-II is true ; Statement-II is correct explanation for Statement-I

  2. Statement-I is true, Statement-II is true ; Statement-II is NOT a correct explanation for statement-I

  3. Statement-I is true, Statement-II is false

  4. Statement-I is false, Statement-II is true
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For Statement-I, if roots are n and n+1, the equation is (x-n)(x-n-1) = x^2 - (2n+1)x + n(n+1) = 0. Then b = 2n+1 and c = n^2+n. The discriminant b^2-4c = (2n+1)^2 - 4(n^2+n) = 4n^2+4n+1-4n^2-4n = 1. Statement-II is true because for odd a, b, c, the discriminant b^2-4ac is odd, ensuring real and distinct roots, but it does not explain Statement-I.

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