Quadratic equation ( need help) – Khan Academy Help Center - Dutch (BETA)

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Tyler

11 april 2017 20:36

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The question is "For what values of a will the following quadratic equation y=ax(Squared) + 24x + 6 have exactly two roots."

It was from a test and I still can't figure it out.

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Flora

14 april 2017 17:57
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Hello,

I'm not an English speaker, so I'm sorry if I don't write very well (especially because it's not "common" language haha)

So, to solve this problem, I don't know if you know "rho" (it's the name of the Greek letter; I've just searched about the name in English, but I don't find, anyway).

Well, you may know, so simply, you have to calculate "rho", which would be

rho = b² - 4*a*c = 24² - 4*a*6 = 24² -24a = 24 (24 - a)

and you know that there are exactly two (different) roots when "rho" is strictly positive (so not equals to zero).

Then , rho > 0 <=> 24 - a > 0 <=> 24 > a <=> a < 24

Then the answer for this question is a<24 (if I did it right)

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