perplexus.info :: Just Math : An unlikely solution!

An unlikely solution! (Posted on 2024-02-21)

The values p and q in the quadratic expression 2x² - px + q are determined by throwing two standard fair cubical dice, one red and one blue.

p is given by the value shown by the red die and q is given by the value shown on the blue die.

What is the probability that the equation 2x² - px + q = 0 will have a solution that is a prime number?

No Solution Yet Submitted by Danish Ahmed Khan

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Solution

| Comment 2 of 4 |

There are 36 possible (p,q) pairs.

But to have a real root, p^2 > 8q; so there are only 10 p,q pairs that meet this condition. I also checked to see if any of the imaginary roots happened to have a modulus, or magnitude that would be an integer and prime. But none did.

Both (5,2) and (6,4) have 2 as a root.

The requested probability is 2/36 or 1/18.

Posted by Larry on 2024-02-21 12:19:31

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