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# Finding roots - C1 Watch

1. I have this question, but I just can't get the right answer. I dunno if I'm doing the wrong method or just stupid mistakes:

Find the roots of 2x^2 - 4x - 3 = 0

I use completing the square method, by taking the coefficient of x out first:

2(x^2 - 4x -3) = 0

Then factorise that:

2((x - 2)^2 - 7) = 0

Then take the 7 over:

2(x - 2)^2 = 7

And then I'm not really sure what to do so I divide both sides by 2:

(x - 2)^2 = 7/2

Then root both sides and then add 2 to get the final answer of 2+/- (rt) 7/2.

However, the answer is apparently 1 +/- (rt) 10/2.

HELP!!??
2. (Original post by Conal09)
I have this question, but I just can't get the right answer. I dunno if I'm doing the wrong method or just stupid mistakes:

Find the roots of 2x^2 - 4x - 3 = 0

I use completing the square method, by taking the coefficient of x out first:

2(x^2 - 4x -3) = 0

Then factorise that:

2((x - 2)^2 - 7) = 0

Then take the 7 over:

2(x - 2)^2 = 7

And then I'm not really sure what to do so I divide both sides by 2:

(x - 2)^2 = 7/2

Then root both sides and then add 2 to get the final answer of 2+/- (rt) 7/2.

However, the answer is apparently 1 +/- (rt) 10/2.

HELP!!??
2x^2 - 4x - 3 does not = 2(x^2 - 4x -3)

multiply it out and you get 2x^2 - 8x - 6
3. The very first line is wrong; try multiply it out to see why.
4. oh

Even so, I still don't get the right answer. Now I get 1 +/- (rt) 1.25
5. (Original post by Conal09)
oh

Even so, I still don't get the right answer. Now I get 1 +/- (rt) 1.25
6. why dont u just put it in quadratic equation?
7. (Original post by EEngWillow)
2(x^2 - 2x - 3/2) = 0

2((x - 1)^2 - 1 - 3/2 = 0

2(x - 1)^2 = 2 1/2

(x - 1)^2 = 1 1/4

x - 1 = +/- (rt) 1 1/4

x = 1 +/- (rt) 1 1/4

Bound to be something wrong in there.
8. (Original post by Conal09)
2(x^2 - 2x - 3/2) = 0

2((x - 1)^2 - 1 - 3/2 = 0

2(x - 1)^2 = 2 1/2

(x - 1)^2 = 1 1/4

x - 1 = +/- (rt) 1 1/4

x = 1 +/- (rt) 1 1/4

Bound to be something wrong in there.
Is that (2 and a half) or 2(1/2)?
If the latter, there's your problem (What's 2(1 + 3/2). Otherwise your problem is the next line.
9. (Original post by Conal09)
2(x^2 - 2x - 3/2) = 0

2((x - 1)^2 - 1 - 3/2 = 0

2(x - 1)^2 = 2 1/2

(x - 1)^2 = 1 1/4

x - 1 = +/- (rt) 1 1/4

x = 1 +/- (rt) 1 1/4

Bound to be something wrong in there.
2((x - 1)^2 - 1 - 3/2) = 0 missing bracket
so
(x - 1)^2 - 1 - 3/2 = 0
then
(x - 1)^2 = 5/2 (I recommend you leave it as a fraction)
10. (Original post by EEngWillow)
Is that (2 and a half) or 2(1/2)?
If the latter, there's your problem (What's 2(1 + 3/2). Otherwise your problem is the next line.
No, it's 2 and a half.
11. (Original post by gdunne42)
2((x - 1)^2 - 1 - 3/2) = 0 missing bracket
so
(x - 1)^2 - 1 - 3/2 = 0
then
(x - 1)^2 = 5/2 (I recommend you leave it as a fraction)
And this still gives me the same answer anyway since 5/2 divided by 2 = 1 1/4
12. If you can't complete the square, use the formula. So the roots are given by and
13. (Original post by MostCompetitive)
If you can't complete the square, use the formula. So the roots are given by and
okay, I got it thanks. I didn't really give that method a thought cos you usually have to use calculators
14. There seems to be a problem with taking the 2 outside the brackets. I'd try just taking the first line and dividing the whole lot by 2, so you just get an x2 term, the 2 disappears and it can cause no further problems.
15. (Original post by Conal09)
okay, I got it thanks. I didn't really give that method a thought cos you usually have to use calculators
You only have to use a calculator when you're not going to leave the roots in surd form. You're welcome.
16. (Original post by Conal09)
okay, I got it thanks. I didn't really give that method a thought cos you usually have to use calculators
Since you have the answer now I'm just going to post up the CTS solution.

17. I hope this isn't taken the wrong way.

Solving quadratics isn't really too difficult, and this one should be fairly straightforward to solve both ways pretty quickly. It isn't that one way is better than the other - you need to be equally happy with both.

It is worth becoming familiar with the techniques, so that when you see a quadratic in the exam, your little heart skips a beat as you know you have got 100% on that question. Honestly, you can get there without too much effort.

So if I were you I'd take 20 questions like that and solve each of them both ways. If towards the end of the 20, you are getting them all right in less than a couple of minutes each, then stop, pat yourself on the back and tell yourself you have got it. If not - try another 10.
18. (Original post by Conal09)
I have this question, but I just can't get the right answer. I dunno if I'm doing the wrong method or just stupid mistakes:

Find the roots of 2x^2 - 4x - 3 = 0

I use completing the square method, by taking the coefficient of x out first:

2(x^2 - 4x -3) = 0

Then factorise that:

2((x - 2)^2 - 7) = 0

Then take the 7 over:

2(x - 2)^2 = 7

And then I'm not really sure what to do so I divide both sides by 2:

(x - 2)^2 = 7/2

Then root both sides and then add 2 to get the final answer of 2+/- (rt) 7/2.

However, the answer is apparently 1 +/- (rt) 10/2.

HELP!!??
I'm doing C1 also, when I get a completing the square question with a coefficient in front of x^2 I find it much less confusing to divide the whole thing through by 2 rather than taking 2 outside of the brackets like you did. You get some pretty nasty fractions, but it all works out in the end.

Alternatively, you could just use the quadratic formula if your surd arithmetic is good.
19. (Original post by EEngWillow)
Since you have the answer now I'm just going to post up the CTS solution.

Can you just confirm this for me? So you have -2 1/2 and then, to get -5, you multiply through by 2? And in doing so you get 2(x-1)^2? That's where I went wrong in that method
20. Fail with the BOLD lol, but you know where I mean

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