Question

Write a polynomial of lowest degree with zeros 1/3 (multiplicity 2) and -1/4 (multiplicity 1) and with f(0)=-3

Answer 1

Answer:

Step-by-step explanation:

y = C(x - 1/3)(x - 1/3)(x + 1/4)

y = C(x² - 2/3x + 1/9)(x + 1/4)

y = C(x³ - 2/3x² + 1/4x² + 1/9x - 1/6x + 1/36)

y = C(x³ - 5/12x² - 1/18x + 1/36)

now to account for the y intercept (x = 0)

-3 = C((0)³ - 5/12(0)² - 1/18(0) + 1/36)

-3 = C(1/36)

C = -108

distribute the C term across all variables.

y = -108x³ + 45x² + 6x - 3

we can verify our solution using a plotting calculator.