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Choose all the possible root combinations for a fifth degree polynomial

[Deleted User]

Choose all the possible root combinations for a fifth degree polynomial.
A. 5 non-real roots
B. 1 real root and 4 nonreal roots
C. 2 real roots and 3 nonreal roots
D. 3 real roots and 2 nonreal roots
E. 4 real roots and 1 nonreal root
F. 5 real roots




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    1 Answer

    1. Quizzma Team

      The correct answers are:

      B. 1 real root and 4 nonreal roots

      C. 2 real roots and 3 nonreal roots

      D. 3 real roots and 2 nonreal roots

      E. 4 real roots and 1 nonreal root

      F. 5 real roots

      Explanation: A fifth-degree polynomial can have a maximum of 5 roots, including complex (nonreal) roots. Since complex roots appear in conjugate pairs, the combinations of real and nonreal roots must follow these rules:

      – If there are 5 roots, they can all be real (option F).

      – If there are nonreal roots, they must appear in pairs, hence 1, 3, or 5 real roots are possible:

      – 1 real root must be paired with 4 nonreal roots (option B).

      – 2 real roots can pair with 3 nonreal roots (option C).

      – 3 real roots can pair with 2 nonreal roots (option D).

      – 4 real roots can pair with 1 nonreal root (option E).

      Always remember that the total number of roots must equal the degree of the polynomial!

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