maths-vectors-graph past paper question?

To obtain a graphical solution to the equation x³ - 5.x - 2 = 0 given a plot of y = x³ - 3.x, you need to draw the straight line y = 2.x + 2, since this subtracts from the cubic to give the required equation.

The roots are found at the points of intersection of the two plots. You may take approximate values from the graph itself. If more accurate values are required, the first point of intersection is near x = -2. Substitution of this into the equation indicates that this is an exact root. Dividing out the term (x + 2) gives

x³ - 5.x - 2 = (x + 2).(x² - 2.x - 1)

The second term has roots at x = 1 ± √2,