Answer:
- the roots are unequal (distinct)
- the roots are irrational
- the roots are real
Step-by-step explanation:
A description of the roots of a quadratic can be had by looking at the value of the discriminant: b²-4ac, where a, b, c are the coefficients of the standard-form quadratic.
Here, we have a=3, b=6, c=1 so the discriminant is ...
d = 6² -4(3)(1) = 24
This is a positive integer that is not a perfect square. This value means ...
- the roots are unequal (distinct)
- the roots are irrational
- the roots are real
_____
The interpretation of the discriminant is ...
- d > 0, distinct real roots
- d = 0, one real root with multiplicity 2
- d < 0, complex roots
If d is an integer that is not a perfect square, the roots (or their imaginary part) will be irrational.
