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Find all the rational zeros

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3 Answers

f(x) =3x2 + 2
 
If by rational zeros you mean values of x where f(x) goes to zero, there are none.
 
This is an equation of a parabola whose vertex is at (0, 2).  f(x) never gets closer to 0 than that.
The zeros of 3x^2 + 2 are the values of x that make the expression evaluate to zero.
 
Solve 3x^2 + 2 = 0.
 
Subtract 2 from both sides:
 
3x^2 = -2
 
x^2 = -2/3
 
|x| = i √(2/3)
 
x = ± i (√(6))/3
 
The zeros are complex (imaginary) numbers which are not rational. ("Rational" means a ratio (fraction) of integers.) NOT that it matters to the answer, but here even the coefficients of i are irrational.