The curve y = x³ + 5x − 1 cuts the x-axis at the point (α, 0).
a. By sketching the graph of y = x³ and one other suitable graph, deduce that this is the only point where the curve y = x³ + 5x − 1 cuts the x-axis.

b. Using calculations, show that 0.1< α < 0.5.