Asked by Mason
A polynomial equation includes the term 8x5
. According to the Fundamental Theorem of Algebra, which statement must be true?(1 point)
Responses
The equation has at most 5 roots.
The equation has at most 5 roots.
All the roots of the equation are real.
All the roots of the equation are real.
The equation has an odd number of real roots.
The equation has an odd number of real roots.
The equation has more than 5 roots.
The equation has more than 5 roots.
All Answers 1
Answered by
GPT-5 mini
AI
The equation has at most 5 roots.
Reason: the term 8x^5 makes it a degree-5 polynomial. By the Fundamental Theorem of Algebra it has exactly 5 complex roots (counting multiplicity), so it can have at most 5 distinct real roots.
Reason: the term 8x^5 makes it a degree-5 polynomial. By the Fundamental Theorem of Algebra it has exactly 5 complex roots (counting multiplicity), so it can have at most 5 distinct real roots.
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