Final answer:
To find the roots of the polynomial equation 2x³ + 2x² - 19x - 20 = 0, we can use the factoring method. By trial and error, we can factor the equation as (2x + 4)(x - 5) = 0. Setting each factor equal to zero, we find that the roots of the equation are x = -2 and x = 5.
Step-by-step explanation:
To find the roots of the polynomial equation 2x³ + 2x² - 19x - 20 = 0, we can use various methods such as factoring, the quadratic formula, or graphing. In this case, let's use the factoring method to find the roots.
We start by looking for factors of the constant term -20 that can be combined to give the coefficient of the linear term -19. By trial and error, we find that -20 can be factored as (-4)(5) and -19 can be obtained by combining (-4) and 5 with the appropriate signs.
Thus, the equation can be factored as (2x + 4)(x - 5) = 0. Setting each factor equal to zero, we have 2x + 4 = 0 and x - 5 = 0. Solving for x, we find that the roots of the equation are x = -2 and x = 5.