Problem

Find all possible roots/zeros of the function \(f(x) = x^3 - 3x^2 - 4x + 12\) using Rational Root Theorem (RRT).

Answer

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Answer

Step 4: Substituting these values into the function, we find that the roots of the function are -1, 2, and 6.

Steps

Step 1 :Step 1: According to the Rational Root Theorem (RRT), the possible rational roots of the function can be expressed as \(\frac{p}{q}\), where p is a factor of the constant term (12 in this case) and q is a factor of the leading coefficient (1 in this case).

Step 2 :Step 2: The factors of 12 are \(\pm1, \pm2, \pm3, \pm4, \pm6, \pm12\). Since the leading coefficient is 1, its only factors are \(\pm1\).

Step 3 :Step 3: Thus, the possible rational roots of the function are \(\pm1, \pm2, \pm3, \pm4, \pm6, \pm12\).

Step 4 :Step 4: Substituting these values into the function, we find that the roots of the function are -1, 2, and 6.

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