What's the probability that equation $x^2 + px + 6.9q = 0$ has real solutions

Asked Mar 03 '19 at 20:28

Active Apr 12 '19 at 18:36

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In the square $K = \{(u,v): u,v \in [0,\;9.6]\}$ randomly selected point with coordinates $(p,q)$. What is probability that equation $x^2 + px + 6.9q = 0$ has real solutions?

I was trying to solve this question, but I have no idea how to draw graph. Is there any easy way to solve this probability? Any help appreciate, thanks.

edited Apr 12 '19 at 18:36

Lee David Chung Lin

7,043

asked Mar 03 '19 at 20:28

MCTG

3

A quadratic $ax^2+bx+c=0$ has real solutions when $b^2-4ac\geq0$. In your case, it is when $p^2-27.6q\geq0$, or $p^2\geq27.6q$. You can do a simple integral to find the probability. – Rushabh Mehta Mar 03 '19 at 20:35
Just to make some connections: 29242 is the node for the basic version with all three uniforms being in $[0 , 1]$. There are similar questions where the ranges of the unifs differ: 3182777 , 3545048 , 1528677 , and 877374. – Lee David Chung Lin Feb 13 '20 at 10:03

What's the probability that equation $x^2 + px + 6.9q = 0$ has real solutions

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