For the equation 2x^3 -11x^2 + 12x + 9 = 0 , the root 3 has a multiplicity of a. 1 b. 2 c. 3 explain!

B. 2

Step-by-step explanation:

The multiplicity of a root is the number of times it occurs as a root.

We must solve the equation to find the number of times 3 occurs as a root.

Since we know that 3 is a root, we can use synthetic division to find the other roots.

f(x) = 2x³ -11x² + 12x + 9

3|2   -11     12     9

 |       6    -15    -9

  2   -5      -3      0

So, (2x³ - 11x² + 12x +9)/(x - 3) = 2x² - 5x – 3

Let’s use synthetic division again to see if 3 is a root of this quadratic

3|2    -5    -3

 |       6      3

 2      1      0

So, 2x² - 5x – 3 = (x - 3)(2x + 1), and

2x³ - 11x² + 12x +9 = (x - 3)(x - 3)²(2x+1)

The factor x – 3 appears twice, so the root 3 has a multiplicity of two.

relating to or denoting a system of numbers and arithmetic based on the number ten, tenth parts, and powers of ten.

it alot will look like this 4.4

ou would have 12 of each