MathDB

Polynomial Probability [2011.II.15]

Source:

March 31, 2011

algebrapolynomialprobabilityfloor functionAMCAIMEquadratics

Problem Statement

Let

P(x)=x^2-3x-9

. A real number

x

is chosen at random from the interval

5\leq x \leq 15

. The probability that

\lfloor \sqrt{P(x)} \rfloor = \sqrt{P(\lfloor x \rfloor )}

is equal to

\dfrac{\sqrt{a}+\sqrt{b}+\sqrt{c}-d}{e}

, where

a,b,c,d

and

e

are positive integers and none of

a,b,

or

c

is divisible by the square of a prime. Find

a+b+c+d+e

.

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