Finding Zeros of a Polynomials Graphically

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What are the zeros of a polynomial?

Back

The zeros of a polynomial are the values of x for which the polynomial equals zero. They are the x-intercepts of the graph.

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How can you find the zeros of a polynomial graphically?

Back

You can find the zeros of a polynomial graphically by identifying the points where the graph intersects the x-axis.

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What does it mean if a polynomial has multiple zeros at the same x-value?

Back

It means that the polynomial touches the x-axis at that point but does not cross it, indicating a repeated root.

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What is the factored form of a polynomial?

Back

The factored form of a polynomial expresses it as a product of its linear factors, such as (x - a)(x - b)...

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How do you determine the number of real zeros from a polynomial's graph?

Back

Count the number of times the graph intersects the x-axis. Each intersection represents a real zero.

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What is the significance of the degree of a polynomial in relation to its zeros?

Back

The degree of a polynomial indicates the maximum number of real zeros it can have.

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What is a polynomial function?

Back

A polynomial function is a mathematical expression involving a sum of powers in one or more variables multiplied by coefficients.

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What is the relationship between the zeros and the factors of a polynomial?

Back

Each zero of a polynomial corresponds to a factor of the form (x - zero).

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How can you verify the zeros of a polynomial?

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You can verify the zeros by substituting them back into the polynomial equation to see if it equals zero.

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What is a multiplicity of a zero?

Back

Multiplicity refers to the number of times a particular zero is repeated in a polynomial.