Find the zeros and their multiplicities for the function ( f(x) = 2x^3 - 3x^2 - 11x + 6 ).

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Accepted Answer

Step:1 ：Step 1: Let&#x27;s set the function equal to zero and solve for x. That is, solve ( 2x^3 - 3x^2 - 11x + 6 = 0 ).Step:2 ：Step 2: Notice that the cubic polynomial can be factored as ( (x-1)(2x+1)(x-3) = 0 ).Step:3 ：Step 3: Setting each factor equal to zero gives the zeros x = 1, x = -1/2, and x = 3.Step:4 ：Step 4: Since each zero appears only once in the factored form of the polynomial, each zero has multiplicity 1.

Answer

Step: 1 ：Step 1: Let&#x27;s set the function equal to zero and solve for x. That is, solve ( 2x^3 - 3x^2 - 11x + 6 = 0 ).Step: 2 ：Step 2: Notice that the cubic polynomial can be factored as ( (x-1)(2x+1)(x-3) = 0 ).Step: 3 ：Step 3: Setting each factor equal to zero gives the zeros x = 1, x = -1/2, and x = 3.Step: 4 ：Step 4: Since each zero appears only once in the factored form of the polynomial, each zero has multiplicity 1.

Find the zeros and their multiplicities for the function \( f(x) = 2x^3 - 3x^2 - 11x + 6 \).

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