upteto17 q122

122If the roots of the equation x² - bx + c = 0 are two consecutive integers, then b² - 4c is

Option : A
Explanation : 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

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