<PRE><B>Question 507247</B>
Which of the following polynomials is prime over the set of rational numbers?
---
x = (-b/(2a)] +- [sqrt(b^2-4ac)]/(2a),
Check the discriminant (b^2-4ac) for each of the quadratics.
If b^2-4ac is not a perfect square the quadratic is prime over the rationals.

------------ 
a.x^2-13x-36
13^2-4*36 = 25 
--------------------
b.x^2-5x-36
5^2 - 4*-36 = 169
---------------------
c.x^2+15x+36
15^2 -4*36 = 225 - 144 = 81
-------------------------
d.x^2+20x+36
20^2-4*36 = 16
============
Conclusion: None of those quadratics is prime over the rationals. 

==============
Cheers,
Stan H.</PRE>