Q. 12

# Mark the Correct alternative in the following:If the roots of are two consecutive integers, then isA. 0B. 1C. 2D. None of these

given that roots are consecutive, let they be a, a+1

From the formula for quadratic equation,

(x - a)(x - a - 1)
= x2 - (a + 1)x - ax + a(a + 1)
= x2 - (2a + 1)x + a(a + 1)
then
b2 - 4c = (2a + 1)2 - 4a(a + 1)
= 4a2 + 1 + 4a - 4a2 - 4a
= 1.

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