Question

What is the difference between a factor of a quadratic equation and a zero of a quadratic equation?  

Answer 1

Generally speaking, a factor is the component of a quadratic equation that gives you a zero.

For example, if you have the quadratic equation \(x^2 - 4\), you can *factor* it into two parts:

\[x^2 - 4 = (x + 2)(x - 2)\]

\(x + 2\) and \(x - 2\) are the *factors*, and they give you the two *zeros*, which are 2 and -2. A zero is the value of x at which the parabola that the quadratic formula describes crosses the y axis (i.e., has a value of 0). A factor is a part of the equation. Multiplying all the factors together gives you the original equation.

Answer 2

Shadowfiend is correct, with one small "oops." The zeros are where the curve of the equation crosses the X-axis, not the y-axis. So in the example above, the parabola crosses the x-axis at 2 and -2; it crosses the y-axis at -4. (The constant term of a polynomial is always the y-intercept.)

Answer 3

Hah! Yes indeed, where it crosses the X axis. Thanks for the catch, LBickford :)

Answer 4

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Answer 5

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Answer 6

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Answer 7

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Answer 8

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Answer 9

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Answer 11

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Answer 12

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Answer 13

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Answer 14

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Answer 15

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Answer 16

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Answer 17

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a.
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b.

Answer 18

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Answer 19

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Answer 20

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Answer 21

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Answer 23

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