### Instruction: Find the discriminant of $3x^2 + \left(3 + \frac 13\right)x + \frac 13$.### Response: The discriminant of a quadratic equation of the form $ax^2 + bx + c$ is $b^2 - 4ac$.
In this case, $a = 3$, $b = 3 + \frac 13$, and $c = \frac 13$.
So, I need to plug these values into the formula and simplify.
$b^2 - 4ac = \left(3 + \frac 13\right)^2 - 4 \cdot 3 \cdot \frac 13$.
To square $3 + \frac 13$, I can use the binomial formula: $(a + b)^2 = a^2 + 2ab + b^2$.
Here, $a = 3$ and $b = \frac 13$.
So, $(3 + \frac 13)^2 = 3^2 + 2 \cdot 3 \cdot \frac 13 + \left(\frac 13\right)^2$.
Simplifying, I get $9 + 2 + \frac 19 = 11 \frac 19$.
Now, I need to subtract $4 \cdot 3 \cdot \frac 13$ from this.
$4 \cdot 3 \cdot \frac 13 = 4$.