Find the nature of roots for the following quadratic equations.

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

Since $\Delta = 9 > 0$, the roots are real and distinct.
The roots are $\boxed{\text{real and distinct}}$.

For $3x^2 - 7x + 4 = 0$, we have $a = 3$, $b = -7$, $c = 4$.

Since $\Delta = 1 > 0$, the roots are real and distinct.
The roots are $\boxed{\text{real and distinct}}$.

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:

The value 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: $\alpha\beta = \frac{c}{a} = \frac{7}{2}$.

Substitute the values of $\alpha + \beta$ and $\alpha\beta$:

The value is $\boxed{-3}$.

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

Given roots are $r_1 = -3$ and $r_2 = 1$.
Sum of roots: $S = r_1 + r_2 = -3 + 1 = -2$.
Product of roots: $P = r_1r_2 = (-3)(1) = -3$.

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