Question

What is the multiplicity of each of the roots or ine grapir on f(x)=-x³+2x²+3x?

Answer 1

The roots for the polynomial f(x) = -x³ + 2x² + 3x are x = 0, x = 1, and x = -3, each with a multiplicity of 1.

Step-by-step explanation:

The question is asking about the multiplicity of the roots for the polynomial function f(x) = -x³ + 2x² + 3x. To find the roots and their multiplicities, we can factor this function if possible, or use computational tools to estimate the roots. This function is a cubic polynomial, so it can have up to 3 real roots, and the multiplicity of each root is the number of times the root appears as a factor of the polynomial.

First, we can attempt to factor the polynomial:

• f(x) = x(-x² + 2x + 3)
• f(x) = x(-x + 1)(x + 3)

So, the roots are x = 0, x = 1, and x = -3. Each root appears only once, so each has a multiplicity of 1.