If f(x) is a 4th degree polynomial, and has 3 real numbers as roots, the other root is?Question 4Select one:a.0b.Realc.Complexd.1e.None of these

To determine the nature of the fourth root of the polynomial $f(x)$ given that it is a 4th degree polynomial with three real roots, we must consider the fundamental theorem of algebra and the properties of polynomials.

Analysis

1. Degree of Polynomial: A 4th degree polynomial has four roots, which can be real or complex.

2. Real Roots: The problem states there are three real roots. For polynomial equations, complex roots come in conjugate pairs if the coefficients are real.

3. Conclusion on Roots: If there are three real roots and one root is required to make four, the fourth root must either be a real number (making it four real roots) or a complex number. However, since complex roots appear in conjugate pairs, having one complex root would necessitate a second complex root, which would increase the root count to five.

Final Answer

Given that it's not possible to have only one complex root when the coefficients are real, the only feasible solution is that the fourth root must indeed be real.

Thus, the answer is: b. Real