Question

Determine the number of zeros of the polynomial function. f(x) = x^3 + 7x^2 + 2

Answer 1

Answer:

  3

Step-by-step explanation:

The fundamental theorem of algebra tells you the number of zeros is equal to the degree of the polynomial.

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application

The given degree-3 polynomial has 3 zeros.

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Additional comment

Descarte's rule of signs tells you the absence of sign changes among the coefficients means that there are no positive real roots. Changing the sign of the one odd-degree term gives one sign change, so there is one negative real root. The other two zeros are complex.

  one negative real zero, and two complex zeros

A graph confirms that the only real zero is negative and irrational, about -7.04.