upteto17 q122
0. If the roots of the equation x2 - bx + c = 0 are two consecutive integers, then b2 - 4c is
- Option : A
- Explanation : (A) Given, equation x2 - bx + c =0
Let roots of the given equation α and α + 1, then sum of roots,
α + (α + 1) = -(-b)/1 = b
⇒ 2α + 1 = b and product of roots, α(α + 1) = c
Now, according to the question,
b2 - 4c = (2α + 1 )2 - 4α(α + 1)
⇒ (4α2 + 1 + 4α) - (4α2 + 4α) = 1
