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Determine the number of zeros of the polynomial function.f(x) = x3 + 4x2 + 1

User SpacePyro
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3 votes

Answer:

1 real zero; 2 complex zeros

Explanation:

A cubic will have 3 zeros. The number of positive and negative real zeros can be determined using Descartes' rule of signs.

There are no sign changes in the coefficients of the function as written, so there are no positive real roots. (+++)

If odd-degree terms have their sign changed, then there is one sign change. (-++) That indicates there is one negative real root.

The remaining two roots will be complex.

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A graphing calculator can confirm this.

Determine the number of zeros of the polynomial function.f(x) = x3 + 4x2 + 1-example-1
User Shawn Lu
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