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An odd degree polynomial equation has:

An odd degree polynomial equation has: Correct Answer At least one real root.

Concept:

  • A polynomial of degree n has exactly n roots.
  • The complex roots of a polynomial always occur in conjugate pairs.

 

Calculation:

Since the complex roots always occur in pairs, we cannot have an odd number of complex roots for any polynomial. Hence, at least one of the (in fact, an odd number of) roots of a polynomial with an odd degree must be real.

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