Question

A polynomial function has a root of -4 with multiplicity 4, a root of -1 with multiplicity 3, and a root of 5

multiplicity 6. If the function has a positive leading coefficient and is of odd degree, which could be the
function?
8
6
4
2
W
-8 -6
-6-
Mark this and return
£
6
FA
-4 6 8 X
Save and Exit
Next

Answer 1

A polynomial function with specific roots and multiplicities can be represented by a function with factors corresponding to the roots and multiplicities given.

Step-by-step explanation:

A polynomial function with a root of -4 with multiplicity 4 means that the function has four factors of (x + 4). Similarly, a root of -1 with multiplicity 3 means that the function has three factors of (x + 1). Finally, a root of 5 with multiplicity 6 means the function has six factors of (x - 5).

The function has a positive leading coefficient, and since it is of odd degree, we know that the multiplicities will add up to an odd number. Therefore, the total multiplicities must be an odd number.

The function could be represented as f(x) = (x + 4)^4 * (x + 1)^3 * (x - 5)^6, where ^ indicates exponentiation.

Learn more about Polynomial function with specified roots and multiplicities