Very good question that includes Polynomials in part (a).

Not sure if using “By Calculator” is allowed at O Levels but otherwise;
(1) use calculator to “cheat” and find root
(2) prove the root using Factor Theorem
(3) use Long division for the other quadratic root if the other roots are not integers cause would require use of the below
(4) solve the quadratic root using quadratic eqn or complete the square

Thereafter just compare the roots and the graph and see that Q is the “middle” root; I have labelled the other roots on the graph for you to see as well.

In part (b),
These questions are very standard. For any min/max questions:
(1) Find dy/dx
(2) equate dy/dx=0 [*notice that for any min/max they are stationary points meaning the gradient is 0 therefore we always say dy/dx=0]
(3) equate the x found in (2) and sub into original Y equation to find corresponding values of Y will give you coordinates of min and max points
(4) find d2y/dx2 and sub the x values in and the identity of the point (min/max) at given value of x.