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# Find all the rational zeros

Formula: 3x^2 +2

### 3 Answers by Expert Tutors

William S. | Experienced scientist, mathematician and instructor - WilliamExperienced scientist, mathematician and...
4.4 4.4 (10 lesson ratings) (10)
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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.
Parviz F. | Mathematics professor at Community CollegesMathematics professor at Community Colle...
4.8 4.8 (4 lesson ratings) (4)
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3 X^2 + 2   is a positive quantity for all values of X, there is no rationl number that makes a positive quantity 0.
Steve S. | Tutoring in Precalculus, Trig, and Differential CalculusTutoring in Precalculus, Trig, and Diffe...
5.0 5.0 (3 lesson ratings) (3)
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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.