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Modulus question!! got stuck

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by vk_vinayak » Mon Aug 27, 2012 6:33 am
nroy347 wrote:Hello...
The question I am unabe to solve..PLEASE HELP !!

If x is an integer, how many possible values of x exist for x^2+|5|x+6 ?
[A] 4
2
[C] 3
[D] 1
[E] 0


Not sure if it is a correct method, but let me try:

I think the equation is x^2+|5|x+6 = 0.

Two cases arise: 5 can be either -5 or +5

Case 1: If +5 => x^2+5x+6 = 0 => x=-2 or x=-3. Plug back these two values in original equation and you can see they work.

Case2: If -5 => x^2-5x+6 = 0 => x=+2 or x=+3. Plug back these two values in original equation and you can see they DO NOT work.

So, we have two solutions. Ans B.
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by nroy347 » Mon Aug 27, 2012 7:03 am
Hi..

No the answer which was given was E!! I got the answer B but I dont know how come E!!
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by vk_vinayak » Mon Aug 27, 2012 7:25 am
I don't think 0 is the answer because the Determinant (b^2 - 4ac) is positive. Therefore two solutions exist.

Maybe experts can help.
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by cypherskull » Mon Aug 27, 2012 8:54 am
Hey Vinayak

I got B as the answer too.

However, I wanted to point out (or rather confirm) the following:
Two cases arise: 5 can be either -5 or +5
As far as I know, |5| cannot have +5 or -5 as its value. Modulus of any positive or negative value is always positive.

This applies to the cases where the value within the modulus is unknown - say |X|. If X (without mods) < 0, |X| = -X. If X > 0, |X| = X.

Besides, I think this question as it stands will always yield B as the answer. Its just a guess but maybe the question is - x^2 + |5x| + 6 = 0.
Regards,
Sunit

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by vk_vinayak » Mon Aug 27, 2012 8:58 am
Thanks, Sunit. I applied + and - by seeing the modulus. You are right, if it is |5| it is just simply 5 not -5.
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