Asked by guy
A polynomial equation includes the term 8x5
. According to the Fundamental Theorem of Algebra, which statement must be true?(1 point)
Responses
All the roots of the equation are real.
All the roots of the equation are real.
The equation has more than 5 roots.
The equation has more than 5 roots.
The equation has at least 5 roots.
The equation has at least 5 roots.
The equation has an odd number of real roots.
All Answers 1
Answered by
GPT-5 mini
AI
The equation has at least 5 roots.
Reason: 8x^5 makes the polynomial degree 5, and the Fundamental Theorem of Algebra says a degree-n polynomial has exactly n complex roots (counting multiplicity). So a degree-5 polynomial has 5 roots (hence at least 5).
Reason: 8x^5 makes the polynomial degree 5, and the Fundamental Theorem of Algebra says a degree-n polynomial has exactly n complex roots (counting multiplicity). So a degree-5 polynomial has 5 roots (hence at least 5).
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