Problem

Given the function \(f(x) = (x + 1)(x - 2)^2(x + 3)^3\), identify the zeros and their multiplicities.

Solution

Step 1 :Firstly, set \(f(x)\) to zero and solve for \(x\): \[0 = (x + 1)(x - 2)^2(x + 3)^3\]

Step 2 :The roots of this equation are the values of \(x\) that make the equation true. Here, the roots are \(-1\), \(2\), and \(-3\), which are obtained by setting each factor equal to zero.

Step 3 :The multiplicity of a root is the number of times it appears in the factored form. In this case, \(-1\) and \(2\) and \(-3\) are the roots, and their multiplicities are 1, 2, and 3 respectively, as indicated by the exponents of the corresponding factors.

From Solvely APP
Source: https://solvelyapp.com/problems/bhXFS4z3FH/

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