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Find a non-zero value for a such that ax^2+8x+4=0 has only one solution.

 Aug 29, 2020
 #1
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The answer is a = -2.

 Aug 29, 2020
 #2
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Find a non-zero value for a such that ax^2+8x+4=0 has only one solution. 

 

(2x + 2)(2x + 2) = 0   so   a = 4 

 

I can't explain how to derive this mathematically. 

When I looked at the problem, I just saw the answer. 

I guess you could call it one form of solving by brute force. 

.

 Aug 29, 2020
 #3
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Hmmm...right. @guest, this is a math question, and therefore it can be done mathematicaly. 

 

How to do without brute force: All you have to do is finish Algebra 1 (or Algebra 2, depending on how your class is taught). 

 

Using discriminants, we see that for there to be only one root, the discriminant has to equal 0. Zero, and ONLY 0. (wrote it two ways just in case)

 

The discriminant can be found with b^2 - 4ac. We know that:

 

b^2 = 64

4ac = 16a

 

So:

 

64 - 16a = 0

- 16a = -64

a = 

 

THE ANSWER ENDS HERE

 

@guest (the second one, not the first one that probably gave a random number): Now, may I ask, how did you right away see that (2x+2)(2x+2) was the answer? I'm not trying to be rude. Maybe you did not see (2x+2)(2x+2), but instead saw that when a = 4, it could be factored into 4(x + 1)^2. Maybe. Maybe you should create an account, (clairvoyant would be a nice user name) so that we could chat, and you could teach me how to see the answer right away wink

 

 

 

:)

 Aug 29, 2020
 #4
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Hello ilorty.  I saw that it was a quadratic, thus would have two roots.  For it to have "one" solution, those two roots would have to be the same, so that makes it something squared.  Then, it was just a matter of factoring an easy quadratic.  There had to be a 2 squared to obtain the 4 at the end.  I recognized that the factors would have to contain 2x to obtain the 8x in the middle (2 • 2x • 2). It takes longer to write it than it did to solve it, LOL.  I did take Algebra 1 & 2 but I don't remember discriminants, but from your example I understand now how it works. 

.

Guest Aug 29, 2020
edited by Guest  Aug 29, 2020
edited by Guest  Aug 29, 2020
 #5
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Very smart, "clairvoyant"

 

I'm sorry if I sounded a bit rude, as I didn't mean to, but I was just trying to prove my point.

 

Though I'm not sure if you are a different guest pretending to be the original answerer...

 

:)

ilorty  Aug 29, 2020
 #6
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a different guest pretending to be the original answerer     

 

LOL, it was me.  I'll reveal a secret... after this, impersonators will be able to mimic me more seemingly authentically, although any reason that someone would want to eludes me.  Below the last line of my text I always place a period, bold it, change the color to white, then make it a subscript.  An impersonator wouldn't have known this before, so you can verify both posts in question were written by yours truly. 

 

This reminds me that once, long ago, I happened across a fact that some scholar - I wish I remembered who - contended that The Odyssey was not written by Homer, but was written by a diffferent Greek named Homer.  I went, Huh? 

.

Guest Aug 30, 2020
 #7
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Homer really is a mystery...

ilorty  Aug 30, 2020

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