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Re: D0141 [#permalink]
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21 Nov 2014, 04:21
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i didn't understand the question. What does equal roots mean?
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21 Nov 2014, 04:49



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Re: D0141 [#permalink]
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15 Feb 2015, 07:56
Hi Bunuel I have a doubt. can anyone help me understand why is the below solution wrong x*x +a*x + 15=0 > x*x +a*x=15 Substituting the above value in below equation we have x*x+ ax b= 0 > 15b=0 > b=15 Thus answer is C@



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Re: D0141 [#permalink]
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16 Feb 2015, 04:45



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Re: D0141 [#permalink]
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16 Feb 2015, 08:57
Bunuel after spending 30 minutes pondering where I went wrong just realized that if I chose b=15 then it becomes the same equation as the second one. In quadratic equations if the constant value changes the root changes. Was taught these things in 8th/9th grade.. This is really embarrassing .. Thanks for replying though atleast my concept got cleared.



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Re: D0141 [#permalink]
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26 Feb 2015, 18:44
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I reasoned through this problem a bit different, but it seems like it landed at the right answer. With a root as x3 and b = 15 for the second equation, you can get to x5 (can't see another way to get a positive 15) and as a result 8 for a. With two same roots and 8 as a, you know it's (xsome number)^2, and 4 is the only number that fits. (X4)^2 results in X2  8x + 16 and as a result 16 fits.
I'm able to follow along Bunel's solution up to the discriminant point; not sure what a discriminant is!



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Re: D0141 [#permalink]
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21 Mar 2015, 10:23
Substitute a=8 in the first equation: x^28xb=0.
Now, we know that it has equal roots thus its discriminant must equal to zero: d=(8)^2+4b=0. Solving for b gives b=16.
How did you get d=(8)^2+4b=0.?



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Re: D0141 [#permalink]
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22 Mar 2015, 06:18
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Re: D0141 [#permalink]
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10 Aug 2015, 16:31
so b^24ac becomes (8)^2+4b? what happens to the negative and the a?



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Re D0141 [#permalink]
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16 Aug 2015, 06:35
I think this is a highquality question and the explanation isn't clear enough, please elaborate. Please explain how d=(−8)2+4b=0 comes in the question.Kindly explain.



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Re: D0141 [#permalink]
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17 Aug 2015, 04:14



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Re: D0141 [#permalink]
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03 Oct 2015, 07:11
Bunuel wrote: Official Solution:
The equation \(x^2 + ax  b = 0\) has equal roots, and one of the roots of the equation \(x^2 + ax + 15 = 0\) is 3. What is the value of b?
A. \(\frac{1}{64}\) B. \(\frac{1}{16}\) C. \(15\) D. \(16\) E. \(64\)
Since one of the roots of the equation \(x^2 + ax + 15 = 0\) is 3, then substituting we'll get: \(3^2+3a+15=0\). Solving for \(a\) gives \(a=8\). Substitute \(a=8\) in the first equation: \(x^28xb=0\). Now, we know that it has equal roots thus its discriminant must equal to zero: \(d=(8)^2+4b=0\). Solving for \(b\) gives \(b=16\).
Answer: D Dear Bunuel or Engr2012Can you explain how you plugged in the values: for the expression b^2−4ac which is called discriminant: I understand if it has same roots, then d must equal 0. But I do not understand the following because you should be plugging in a = 8 into the equation above, ... i can not follow how you then have 8^2 which should be b^2. And what about variable c? Please help. \(d=(8)^2+4b=0\). Solving for \(b\) gives \(b=16\).
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reto wrote: Bunuel wrote: Official Solution:
The equation \(x^2 + ax  b = 0\) has equal roots, and one of the roots of the equation \(x^2 + ax + 15 = 0\) is 3. What is the value of b?
A. \(\frac{1}{64}\) B. \(\frac{1}{16}\) C. \(15\) D. \(16\) E. \(64\)
Since one of the roots of the equation \(x^2 + ax + 15 = 0\) is 3, then substituting we'll get: \(3^2+3a+15=0\). Solving for \(a\) gives \(a=8\). Substitute \(a=8\) in the first equation: \(x^28xb=0\). Now, we know that it has equal roots thus its discriminant must equal to zero: \(d=(8)^2+4b=0\). Solving for \(b\) gives \(b=16\).
Answer: D Dear Bunuel or Engr2012Can you explain how you plugged in the values: for the expression b^2−4ac which is called discriminant: I understand if it has same roots, then d must equal 0. But I do not understand the following because you should be plugging in a = 8 into the equation above, ... i can not follow how you then have 8^2 which should be b^2. And what about variable c? Please help. \(d=(8)^2+4b=0\). Solving for \(b\) gives \(b=16\). Once you get a =8 and know that as the discriminant for equal roots = 0 > from the original equation\(x^2+axb=0\), the discriminant is = \(a^24(1)(b)=0\) >\(a^2+4b=0\)> substitute \(a =8\) , \((8)^2+4b=0\) > \(64+4b=0\) > \(b = 16\).



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Re: D0141 [#permalink]
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01 Dec 2015, 19:58
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You can still get this problem if you're like me and aren't totally comfortable with the concept of a discriminant.
Once you get to the point where you figure out a = 8, rephrase the x^2 + ax  b = 0 equation as x^2  8x  b = 0 and simply plug in the answer choices, then factor. The equation has "equal roots" so its going to take the form of (x+y)^2 or (xy)^2.
Starting with C, the equation x^2  8x + 15 = 0, but since 15 isn't a perfect square this clearly won't yield equal roots while adding up to 8x.
Moving on to D, the equation becomes x^2  8x + 16 = 0; or (x4)(x4)=0. It fits.
The other choices don't fit as they don't add up to 8x when factored/foiled.



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Re D0141 [#permalink]
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08 Dec 2015, 05:23
I think this is a highquality question and I agree with explanation. Great question! But it appears to be more of a 700 range and not 600.
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Re: D0141 [#permalink]
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21 Feb 2016, 10:29
bdawg2057 wrote: You can still get this problem if you're like me and aren't totally comfortable with the concept of a discriminant.
Once you get to the point where you figure out a = 8, rephrase the x^2 + ax  b = 0 equation as x^2  8x  b = 0 and simply plug in the answer choices, then factor. The equation has "equal roots" so its going to take the form of (x+y)^2 or (xy)^2.
Starting with C, the equation x^2  8x + 15 = 0, but since 15 isn't a perfect square this clearly won't yield equal roots while adding up to 8x.
Moving on to D, the equation becomes x^2  8x + 16 = 0; or (x4)(x4)=0. It fits.
The other choices don't fit as they don't add up to 8x when factored/foiled. Thanks, This made my day.



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Re D0141 [#permalink]
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24 May 2016, 21:14
I think this is a highquality question and the explanation isn't clear enough, please elaborate. I don't understand what is "we know that it has equal roots thus its discriminant must equal to zero: d=(−8)2+4b=0d=(−8)2+4b=0."means.



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Re: D0141 [#permalink]
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