f(x) = 20x³ + 8x² − 7x − 3

a. The equation 20x³ + 8x² − 7x − 3 = 0 has exactly two roots.

Without factorising the cubic equation, show, by calculation, that one of these roots is between 0.5 and 1.

b. Show, by sketching the graph of y = f(x) for −1 ≤ x ≤ 1, that the smaller root is between −1 and 0.

c. Explain why it is not necessary to use a numerical method to find the two solutions of this equation.