Question

Find the equation of the polynomial described below. Degree 4. Root of multiplicity 2 at x = 4, and a root of multiplicity 1 at x = 1 and x = -2. y-intercept at (0, -3).

Options:
a. y = (x^2 - 4x)(x + 2)(x - 1)
b. y = (x^2 - 4)(x + 2)(x - 1)
c. y = (x^2 - 4x)(x + 2)(x - 1)^2
d. y = (x^2 - 4)(x + 2)(x - 1)^2

Answer 1

The equation of the polynomial described is y = (x^2 - 4x)(x + 2)(x - 1)^2

Step-by-step explanation:

The equation of the polynomial described is option c. y = (x^2 - 4x)(x + 2)(x - 1)^2

To find the equation, we use the given roots and their multiplicities. Since the root 4 has a multiplicity of 2, it means that the factors (x-4) and (x-4) should be present. Similarly, the roots 1 and -2 with multiplicities 1 mean that the factors (x-1) and (x+2) should be present. Finally, we use the y-intercept (0,-3) to find the constant term.

Therefore, the equation is y = (x^2 - 4x)(x + 2)(x - 1)^2