Alan

To clarify, I mean you have included the i under the square root signs, which the original question doesn't do.

You must have used sqrt2i) instead of sqrt(2)i to get your result Guest #5.

Asinus, the variance is 12, the standard deviation is the square root of the variance.

This is just:    y = -4x/3 - 1

.

There is no equation here, so we can't say if the x,y pairs are solutions!

There are 7 odd numbers and 6 even numbers in the range.  To get an odd product both of the chosen random numbers must be odd.  

probability that the first number is odd: p1 = 7/13

probability that the second number is odd: p2 = 6/12 → 1/2  (I assume the word "distinct" means the first number is removed from the set before choosing the second number).

Overall probability:   p1*p2 = 7/13*1/2 → 7/26 ≈ 0.269

.

The neatest solution yet!

I guess that just saying "a maximum of n roots" isn't as useful in advanced analysis.

Because it isn't true that every polynomial of degree n has n different roots.  They have n roots, some of which might be repeated.

 I guess the reason the FTOA specifies it in this way is so that there is no need to include an extra statement for those cases where there are repeated roots.  There might be a deeper mathematical reason, but, if so, I'm not aware of it.

x + 1/x = sqrt(11)

Square both sides

x² + 2*x*1/x + 1/x² = 11

x² + 2 + 1/x² = 11

x² + 1/x² = 9

.