Determine the roots of 3x² − 5x − 7 = 0 from the graph.

The roots of the equation $3x^2 - 5x - 7 = 0$ are the x-intercepts of the graph $y = 3x^2 - 5x - 7$, which are the points where the curve crosses the x-axis (where $y=0$).
From the graph, the curve crosses the x-axis at approximately $x = -0.9$ and $x = 2.6$.

a) (i) The roots are $\boxed{x = -0.9 \text{ and } x = 2.6}$.

The minimum value of $y$ for this parabola (which opens upwards) is at its vertex, the lowest point on the curve.
From the graph, the lowest point on the curve is at $y = -9$.

a) (ii) The minimum value of $y$ is $\boxed{y = -9}$.

To find the gradient of the curve at $x=2$ from the graph, we need to find the gradient of the tangent line to the curve at $x=2$. The image provides a calculation using two points on what appears to be a tangent line or a secant line approximating the tangent. The points used are $(x_1, y_1) = (1.30, -10)$ and $(x_2, y_2) = (3, 1.5)$.

The formula for the gradient (slope) is:

$$m = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1}$$

Substitute the given points:

$$m = \frac{1.5 - (-10)}{3 - 1.30}$$ $$m = \frac{1.5 + 10}{1.70}$$ $$m = \frac{11.5}{1.70}$$ $$m \approx 6.7647$$

Rounding to one decimal place, the gradient is 6.8.

a) (iii) The gradient of the curve at point $x=2$ is $\boxed{\approx 6.8}$.