If a ≠ b and a : b is the duplicate ratio of (a + c) and (b + c), show that a, c and b are in continued proportion.

What number should be subtracted from 2x³ - 5x² + 5x + 8 so that the resulting polynomial has a factor 2x - 3 ?

Show that 2x + 7 is a factor of 2x³ + 7x² - 4x - 14. Hence, solve the equation :

2x³ + 7x² - 4x - 14 = 0.