Final answer:
To find the value of a³ + b³, we need to use the formula for the sum of cubes: a³ + b³ = (a + b)(a² - ab + b²). In this case, the zeroes of the polynomial x² - 11x + 30 are a = 3 and b = 10. Now, substitute these values into the formula: 3³ + 10³ = (3 + 10)(3² - 3 × 10 + 10²) = 13 × (9 - 30 + 100) = 13 × 79 = 1027.
Step-by-step explanation:
To find the value of a³ + b³, we need to use the formula for the sum of cubes: a³ + b³ = (a + b)(a² - ab + b²). In this case, the zeroes of the polynomial x² - 11x + 30 are a = 3 and b = 10 (you need to solve the polynomial to find the values of a and b).
Now, substitute these values into the formula: 3³ + 10³ = (3 + 10)(3² - 3 × 10 + 10²) = 13 × (9 - 30 + 100) = 13 × 79 = 1027.