SOLUTION: Please help me solve this problem. Show that the equation {{{ 5x^3+3x+2=0}}} lacks rational solutions Thanks in advance!

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Please help me solve this problem. Show that the equation {{{ 5x^3+3x+2=0}}} lacks rational solutions Thanks in advance!      Log On


   

Question 766253: Please help me solve this problem.
Show that the equation +5x%5E3%2B3x%2B2=0 lacks rational solutions
Thanks in advance!
Answer by reviewermath(1029) About Me  (Show Source):
You can put this solution on YOUR website!
Q:
Show that the equation +5x%5E3%2B3x%2B2=0 lacks rational solutions
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A:
In +5x%5E3%2B3x%2B2=0, a = 5, b =3 and c = 2.
The discriminant is b%5E2+-+4ac = 3%5E2+-+4%285%29%282%29 = -31 < 0.
If the discriminant is less than zero, then the quadratic equation lacks real
number solutions. Rational numbers is a subset of real numbers so the quadratic equation also lacks rational solutions.