Question 766253
Q:
Show that the equation {{{ 5x^3+3x+2=0}}} lacks rational solutions
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A:
In {{{ 5x^3+3x+2=0}}}, a = 5, b =3 and c = 2.
The discriminant is {{{b^2 - 4ac}}} = {{{3^2 - 4(5)(2)}}} = -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.