Question

Write a third-degree polynomial function with roots of -1 and 3 - √3.

a) f(x) = (x + 1)(x - (3 - √3))(x - (3 + √3))
b) f(x) = (x - 1)(x + (3 - √3))(x + (3 + √3))
c) f(x) = (x - 1)(x - (3 - √3))(x - (3 + √3))
d) f(x) = (x + 1)(x + (3 - √3))(x + (3 + √3))

Answer 1

The correct answer is f(x) = (x + 1)(x - (3 - √3))(x - (3 + √3)) (option a). To find the third-degree polynomial function with roots of -1 and 3 - √3, we need to use the fact that the roots of a polynomial are the values of x that make the function equal to zero. So, since -1 and 3 - √3 are roots, the factor of the polynomial must be (x + 1)(x - (3 - √3))(x - (3 + √3)). Multiplying these factors together gives us the third-degree polynomial function with the given roots.

Step-by-step explanation:

The correct answer is f(x) = (x + 1)(x - (3 - √3))(x - (3 + √3)) (option a).

To find the third-degree polynomial function with roots of -1 and 3 - √3, we need to use the fact that the roots of a polynomial are the values of x that make the function equal to zero. So, since -1 and 3 - √3 are roots, the factor of the polynomial must be (x + 1)(x - (3 - √3))(x - (3 + √3)). Multiplying these factors together gives us the third-degree polynomial function with the given roots.