Zeroes of cubic polynomial

In summary, the zeroes of a cubic polynomial are the values of the variable that make the polynomial equal to zero. A cubic polynomial can have a maximum of three zeroes, which can be found using the Rational Zero Theorem or by graphing the polynomial. These zeroes can be real or imaginary, occurring in conjugate pairs if the polynomial has real coefficients. The zeroes also represent the x-intercepts of the polynomial's graph, with a y-value of zero at these points.
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You can read $\alpha + \beta + \gamma $, $\alpha\beta +\alpha \gamma + \beta \gamma$ and $\alpha \beta \gamma$ off from the polynomial.

Now what's $(\alpha+\beta)+(\alpha+\gamma)+(\beta+\gamma)$?

And what's $(\alpha+\beta)(\alpha+\gamma)(\beta+\gamma)$?

And finally $(\alpha+\beta)(\alpha+\gamma)+(\beta+\gamma)(\alpha + \beta)+(\alpha+\gamma)(\beta+\gamma)$?Those questions all seem to be an exercise in Vietas formulas.
 
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1. What are the zeroes of a cubic polynomial?

The zeroes of a cubic polynomial are the values of the variable that make the polynomial equal to zero.

2. How many zeroes can a cubic polynomial have?

A cubic polynomial can have a maximum of three zeroes.

3. How can I find the zeroes of a cubic polynomial?

One method is by using the Rational Zero Theorem, which involves finding the possible rational roots of the polynomial and then using synthetic division to check for actual zeroes. Another method is by graphing the polynomial and finding the x-intercepts.

4. Can a cubic polynomial have imaginary zeroes?

Yes, a cubic polynomial can have imaginary zeroes, which occur in conjugate pairs if the polynomial has real coefficients.

5. What is the relationship between the zeroes of a cubic polynomial and its graph?

The zeroes of a cubic polynomial represent the x-intercepts of its graph. This means that the graph will intersect the x-axis at these points, and the y-value of the graph at these points will be equal to zero.

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