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# Further pure 1 question watch

1. Hi this is my first time on this so I may not explain things very well but the question is :

Find the solution of the following equation

x^2 +4x+7 =0

(-4 +/- the square root of 16 - 28) / 2

so i had (-4 +/- sqrt of -12) / 2

sqrt -12 equals root 4 multiplied by sqrt of -3

the sqrt of 4 is +/- 2 and sqrt of -3 = sqrt 3i

which equals (-4 +/- +/- 2 sqrt 3i)/2

so it is -2 +/- +/- root 3i.

From this I thought that it could be + or - root 3i. But it seems that it is only + root 3i after subbing the answer back into the equation. Why can't you + and then -, why must it be + and then + or - and then -, which is ultimately a plus.
2. Because each positive/negative one is a specific solution, so if you sub in a postive one and then a negative one, you're basically subbing in two different solutions.
3. (Original post by Sifi28)
Hi this is my first time on this so I may not explain things very well but the question is :

Find the solution of the following equation

x^2 +4x+7 =0

(-4 +/- the square root of 16 - 28) / 2

so i had (-4 +/- sqrt of -12) / 2

sqrt -12 equals root 4 multiplied by sqrt of -3

the sqrt of 4 is +/- 2 and sqrt of -3 = sqrt 3i

which equals (-4 +/- +/- 2 sqrt 3i)/2

so it is -2 +/- +/- root 3i.

From this I thought that it could be + or - root 3i. But it seems that it is only + root 3i after subbing the answer back into the equation. Why can't you + and then -, why must it be + and then + or - and then -, which is ultimately a plus.
Are you sure (see what I've put in bold)? , so how did you get this: ?
4. (Original post by MostCompetitive)
so how did you get this: ?
What's wrong with that?

5. (Original post by soutioirsim)
What's wrong with that?

So it is - not the square root of 3i as the OP has said. Latex makes things a lot easier to understand.
6. I'm still confused sorry. I don't understand why, as it could be +/- -2 or +/- 2, which would surely mean 2 solutions doesnt it
7. (Original post by MostCompetitive)
So it is - not the square root of 3i as the OP has said
Well that was plainly obvious anyway from his working lol.
8. yeah sorry i meant, i sqrt 3, i didnt mean the square root of the whole 3i
9. (Original post by soutioirsim)
Well that was plainly obvious anyway from his working lol.
I guess I misinterpreted it. He should have used latex since I didn't look that closely at his workings.
10. (Original post by Sifi28)
I'm still confused sorry. I don't understand why, as it could be +/- -2 or +/- 2, which would surely mean 2 solutions doesnt it
It's not +/-2, it should only be +/- the imaginary part:

I hope that clears it up.

So it's always -2.
11. I'm so sorry, i didnt mean +/- 2 i mean +/- 3i.

I've now just realised that my text book is wrong. It said there was only one solution -2 + i sqrt 3. I thought there were two and when I subbed it in I made a mistake and didnt understand why one of them didnt work. Stupid Text books. Thanks for the help, much appreciated

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Updated: March 25, 2011
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