SOLUTION: Which of the following polynomials is prime over the set of rational numbers? a.x^2-13x-36 b.x^2-5x-36 c.x^2+15x+36 d.x^2+20x+36

Algebra ->  Real-numbers -> SOLUTION: Which of the following polynomials is prime over the set of rational numbers? a.x^2-13x-36 b.x^2-5x-36 c.x^2+15x+36 d.x^2+20x+36      Log On


   

Question 507247: Which of the following polynomials is prime over the set of rational numbers?
a.x^2-13x-36
b.x^2-5x-36
c.x^2+15x+36
d.x^2+20x+36
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Which of the following polynomials is prime over the set of rational numbers?
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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.
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a.x^2-13x-36
13^2-4*36 = 25
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b.x^2-5x-36
5^2 - 4*-36 = 169
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c.x^2+15x+36
15^2 -4*36 = 225 - 144 = 81
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d.x^2+20x+36
20^2-4*36 = 16
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Conclusion: None of those quadratics is prime over the rationals.
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Cheers,
Stan H.