Discriminant question (1 Viewer)

Daq

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I tried using the discriminant for this question but my answer wasn't right, can someone help please?

Screenshot 2025-06-04 at 9.38.49 AM.png
 

Hehehe22

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I might be wrong but I don't think any of these options are correct. @alphxreturns can you explain how you got B?

Any vertical asymptotes for the function y occur when the denominator crosses the x-axis, i.e. when a + bx + 4ax^2 = 0. This function always has a horizontal asymptote, so for only one asymptote, you need to find when there's no vertical asymptote. This means that you need to find values where a + bx + 4ax^2 has no real roots, and you can do this using the discriminant, as you said. That would give you b^2 - 16a^2 < 0, which solves to b < |4a|, or -4a < b < 4a
 

alphxreturns

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I might be wrong but I don't think any of these options are correct. @alphxreturns can you explain how you got B?

Any vertical asymptotes for the function y occur when the denominator crosses the x-axis, i.e. when a + bx + 4ax^2 = 0. This function always has a horizontal asymptote, so for only one asymptote, you need to find when there's no vertical asymptote. This means that you need to find values where a + bx + 4ax^2 has no real roots, and you can do this using the discriminant, as you said. That would give you b^2 - 16a^2 < 0, which solves to b < |4a|, or -4a < b < 4a
looking back on it, I'm wrong.
(B lets there be one and more roots)

I'm looking at it rn and C works. see a>1 so it fits the criteria, tho not directly
 

alphxreturns

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I really don't understand why yall r using bos for math qns. Shove this into caht and you've got solutions 80% of the time
ai is tripping out on this question rn

i had to lead it through (it was very confused) and landed on C after a lot of nudging and hinting

i'd compeltely forgotten abt the horizontal asymptote so thanks @Hehehe22 for catching it
 

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