Find the nature of roots for quadratic equations and evaluate expressions involving roots.

Here, $a=2$, $b=-5$, $c=2$.

Since $\Delta = 9 > 0$, the roots are real and distinct.

Here, $a=3$, $b=-7$, $c=4$.

Since $\Delta = 1 > 0$, the roots are real and distinct.

2) If $\alpha$ and $\beta$ are the roots of the equation $3x^2 - 5x + 4 = 0$, find the value of $\alpha/\beta + \beta/\alpha$.

For $3x^2 - 5x + 4 = 0$, we have $a=3$, $b=-5$, $c=4$.

Sum of roots: $\alpha + \beta = -\frac{b}{a} = -\frac{-5}{3} = \frac{5}{3}$.
Product of roots: $\alpha\beta = \frac{c}{a} = \frac{4}{3}$.

We know that $\alpha^2 + \beta^2 = (\alpha + \beta)^2 - 2\alpha\beta$.
Substitute this into the expression:

To subtract the terms in the numerator, find a common denominator:

The value of $\frac{\alpha}{\beta} + \frac{\beta}{\alpha}$ is $\boxed{\frac{1}{12}}$.

3) If $\alpha$ and $\beta$ are the roots of the equation $2x^2 - 4x + 7 = 0$, find $\alpha^2 + \beta^2$.

For $2x^2 - 4x + 7 = 0$, we have $a=2$, $b=-4$, $c=7$.

Sum of roots: $\alpha + \beta = -\frac{b}{a} = -\frac{-4}{2} = \frac{4}{2} = 2$.
Product of roots: $\alpha\beta = \frac{c}{a} = \frac{7}{2}$.

The value of $\alpha^2 + \beta^2$ is $\boxed{-3}$.

4) Construct and simplify equations whose roots are $-3, 1$.

The constructed quadratic equation is $\boxed{x^2 + 2x - 3 = 0}$.