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 Only real x counted (Posted on 2017-03-01)
Let a and b be chosen at random from {0,1,2,3,4,5,6,7,8,9}.

Find the probability that x^2 + ax + b^2 = 0 will have
at least one real solution.

 No Solution Yet Submitted by Ady TZIDON No Rating

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 solution (spoiler) | Comment 1 of 3
Quadratic a^2 + ax + b^2 = 0 has real root(s) if the discriminant is non-negative, i.e.,

a^2 - 4*b^2 >= 0

a^2 >= 4*b^2

As a and b are both non-negative in the set from which they are chosen,

a >= 2*b

What then is the probability that that will be the case?

Overall there are 100 ways in which a and b can be chosen (assuming equality between the two is allowed). How many of these are successes?

b           a
0        10 choices
1         8 choices
2         6 choices
3         4 choices
4         2 choices
5         0 choices
--
30

The probability is 30%.

 Posted by Charlie on 2017-03-01 10:52:32

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