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<span>You made a mistake either on the polynomial function or on the choices.
I will explain you how to get the answer, using the same polynomial given:
Answer: 3 with multiplicity 2 and 6 with multiplicity 3.
The given polynomial function is f(x)=(x-3)^4 * (x-6)^2
or written with the math tool:
The roots are the x-intercepts of the function. This isthe values of x for which the function is zero. Thus, you have to find the solution to this equation:
The solutions are:
1) (x-3)^4 = 0 => (x-3)=0 => x = 3. The multiplicity of the root is the exponent of the factor, so the multiplicity of this root is 4.
You can understand that if you think that (x-3)^4 = (x-3)(x-3)(x-3)(x-3), which tells you that (x - 3) is 0 for each one of the 4 parenthesis.
2) (x - 6)^2 = 0 => x = 6, with multiplicity 2 (the exponent of the factor x - 6).
Then, the answer is 3 with multiplicity 4 and 6 with multiplicity 2.
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I will explain you how to get the answer, using the same polynomial given:
Answer: 3 with multiplicity 2 and 6 with multiplicity 3.
The given polynomial function is f(x)=(x-3)^4 * (x-6)^2
or written with the math tool:
The roots are the x-intercepts of the function. This isthe values of x for which the function is zero. Thus, you have to find the solution to this equation:
The solutions are:
1) (x-3)^4 = 0 => (x-3)=0 => x = 3. The multiplicity of the root is the exponent of the factor, so the multiplicity of this root is 4.
You can understand that if you think that (x-3)^4 = (x-3)(x-3)(x-3)(x-3), which tells you that (x - 3) is 0 for each one of the 4 parenthesis.
2) (x - 6)^2 = 0 => x = 6, with multiplicity 2 (the exponent of the factor x - 6).
Then, the answer is 3 with multiplicity 4 and 6 with multiplicity 2.
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