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Can someone explain to be in detail what is quadratic inequality? It's rather confusing. Thank you

- Thread starter Lim Y K
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Member warned about posting with little or no prior research

Can someone explain to be in detail what is quadratic inequality? It's rather confusing. Thank you

- #2

jedishrfu

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There are some video tutorials on it that may help:

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Try to find the 2 roots of the quadratic equation and discuss the intervals made of these numbers.

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symbolipoint

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[tex]ax^2+bx+c<0[/tex]or[tex]ax^2+bx+c<=0[/tex]or[tex]ax^2+bx+c>0[/tex]or[tex]ax^2+bx+c>=0[/tex]

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symbolipoint

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For visualisation's sake, is it something like that? The space between the two intersection in the graph is equivalent to the space between he two lines on the number line?

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symbolipoint

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The Mathispower4u (which jedishru posted) video you should find very helpful in understanding what to do with solving a quadratic inequality. The roots of the quadratic expression form the x-number line into three intervals, and any value in each interval can be chosen to test the truth or falsity for the interval.

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symbolipoint

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That step now gives you [itex]x^2+x+1/4[/itex] versus 0, as said, with relation reversed from what it was originally. This quadratic is factorable giving you exactly ONE critical x value.

[itex](x+1/2)^2[/itex]. versus 0. (You did not show on your paper the inequality symbol relating). The critical value is at [itex]x=-1/2[/itex], just one single value, cutting the x-number line into just two intervals. Now, you test each interval, and maybe also you need to test that critical x value of [itex]-1/2[/itex].

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