Find the nature of roots for quadratic equations and calculate if alpha and beta are the roots of the equation 3x2 − 5x + 4 = 0, find the value of alpha/beta + beta/alpha.

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

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

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

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 $3x^2 - 5x + 4 = 0$, $a = 3$, $b = -5$, $c = 4$.
Sum of roots: $\alpha + \beta = -\frac{b}{a} = -\frac{-5}{3} = \frac{5}{3}$.
Product of roots: $\alpha\beta = \frac{c}{a} = \frac{4}{3}$.

The value is $\boxed{\frac{1}{12}}$.

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

For $2x^2 - 4x + 7 = 0$, $a = 2$, $b = -4$, $c = 7$.
Sum of roots: $\alpha + \beta = -\frac{b}{a} = -\frac{-4}{2} = 2$.
Product of roots: $\alpha\beta = \frac{c}{a} = \frac{7}{2}$.

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

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

Sum of roots $= -3 + 1 = -2$.

Product of roots $= (-3)(1) = -3$.

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