Difference between revisions of "Double root"
(Created page with "The '''double root instance''' occurs when a quadratic equation is the square of a binomial, or when its discriminant is equal to <math>0</math>.") |
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The '''double root instance''' occurs when a [[quadratic equation]] is the [[square]] of a [[binomial]], or when its [[discriminant]] is equal to <math>0</math>. | The '''double root instance''' occurs when a [[quadratic equation]] is the [[square]] of a [[binomial]], or when its [[discriminant]] is equal to <math>0</math>. | ||
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+ | ==Example== | ||
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+ | Find all solutions to the quadratic equation <math>3x^2+6x+3=0</math>. | ||
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+ | Plugging the values of <math>a, b</math> and <math>c</math> into the [[quadratic formula]], we get | ||
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+ | <math>\frac{-6\pm\sqrt{6^2-4(3)(3)}}{2(3)}=\frac{-6\pm\sqrt{36-36}}{6}=\frac{-6\pm\sqrt{0}}{6}=\frac{-6}{6}=-1</math> | ||
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+ | so this quadratic has a double root of <math>-1</math>. | ||
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+ | We also could have solved this problem by [[factoring]] a <math>3</math> out of the left side and dividing: | ||
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+ | <math>3(x^2+2x+1)=0 \Longrightarrow x^2+2x+1=0</math> | ||
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+ | and now we plug the [[coeficcients]] into the quadratic formula: | ||
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+ | <math>\frac{-2\pm\sqrt{2^2-4(1)(1)}}{2(1)}=\frac{-2\pm\sqrt{4-4}}{2}=\frac{-2}{2}=-1</math> | ||
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+ | so again, the quadratic has a double root of <math>-1</math>. |
Revision as of 10:54, 15 May 2014
The double root instance occurs when a quadratic equation is the square of a binomial, or when its discriminant is equal to .
Example
Find all solutions to the quadratic equation .
Plugging the values of and
into the quadratic formula, we get
so this quadratic has a double root of .
We also could have solved this problem by factoring a out of the left side and dividing:
and now we plug the coeficcients into the quadratic formula:
so again, the quadratic has a double root of .