Answer:
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
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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.
