JEE MAIN - Mathematics (2005 - No. 53)
If the roots of the equation $${x^2} - bx + c = 0$$ be two consecutive integers, then $${b^2} - 4c$$ equals
$$-2$$
$$3$$
$$2$$
$$1$$
Explanation
Let n and (n + 1) be the roots of x2 $$-$$ bx + c = 0.
Then, n + (n + 1) = b and n(n + 1) = c
$$\therefore$$ b2 $$-$$ 4c = (2n + 1)2 $$-$$ 4n(n + 1)
= 4n2 + 4n + 1 $$-$$ 4n2 $$-$$ 4n = 1
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