C1 simply question but can't be sure of answer..

This is the question:

Solve the equation

x^6 + 26x^3 - 27 = 0

So I got the solutions as -1 and 3; however these do not give zero when you put these values back into the original equation - is there a reason for this?

(edited 13 years ago)

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Reply 1

the greatest

Original post by Dededex

This is the question:

Solve the equation

x^6 + 26x^3 - 27 = 0

So I got the solutions as -1 and 3; however these do not give zero when you put these values back into the original equation - is there a reason for this?

firstly we know that 1 works and is a root of the equation and a solution

so (x-1) is a factor

we also know that -3 is a root and a solution

so (x+3) is a factor

you can then multiply these two factors divide them by the equation using long division, and from your clculations you should get the right answer

Show your working.

how did you get those solutions?

Spoiler

(edited 13 years ago)

Reply 4

Revolution is my Name

Original post by Dededex

is there a reason for this?

It's because they're not the right answers...

Reply 5

dnumberwang

x^6 + 26x^3 - 27 = 0

once you've factorised it to

(x^3 + 27)(x^3 - 1) = 0

x^3 + 27 = 0

and

x^3 - 1 = 0

From there you take the number to the other side so the sign changes

Reply 6

Dededex

Hmm well I let u = x^3 so I had an equation like this:

u^2 + 26u - 27

Which factorises as

(u + 27)(u - 1)

Then I got two solutions for u as -27 and +1.

Therefore x = cube root u so x = -3 or 1

THREAD FAIL

(edited 13 years ago)

Reply 7

Dededex

Yep sorry sorry I factorised it wrong... :blush:

Reply 8

MostCompetitive

The reason why is because you have got the signs mixed up. -3 and 1 are the solutions. It is always best to sub something else in for what is, in this case,

x^3

and then solve it like a normal equation. Remember:

x^6=(x^3)^2

, so you will have a normal quadratic to solve after substituting something in for

x^3

(edited 13 years ago)

Reply 9

WildBerry

I just done this question earlier, didnt help that the mark scheme I had was all wrong so I wasn't sure if it was right. I got those answers, -3 , 1 :smile:

Reply 10

BieberFan

Original post by Dededex

Yep sorry sorry I factorised it wrong... :blush:

This is like the hundreth thread you've made asking for C1 or C2 help. Why bother asking questions about Cambridge? You obviously have no chance whatsoever if you're struggling so much with AS maths. I bet you got your GCSEs by trying hard but it doesn't work like that for the best unis. Grades aren't anywhere near enough to get in.

Can I ask, did you fail the SMC? If so, that's further proof of how impossible this is for you. You'd be lucky to get into kingston...

I'm telling you this so you don't build up false hope. YOU HAVE NO CHANCE, YOU JUST DON'T HAVE THE BRAIN FOR IT!

Reply 11

WildBerry

Original post by BieberFan

What a bloody troll ...

Reply 12

BieberFan

Original post by WildBerry

What a bloody troll ...

Tell me, what part of what I've said is untrue?

Reply 13

Dededex

Original post by BieberFan

Hey hey it's an easy arithmetic error perhaps my only query on the paper, calm down!

Reply 14

BieberFan

Original post by Dededex

Hey hey it's an easy arithmetic error perhaps my only query on the paper, calm down!

And what about the other 200 threads you've started...

Reply 15

Dededex

Original post by BieberFan

And what about the other 200 threads you've started...

That's a massive over exaggeration; whilst it may portray me as an idiot asking pretty simpleton questions, the fact of the matter is I don't care!

If I want to know why the answer to a question is what it is I'm not going to hide in the corner just so I can look smart and superior. That's stupid and won't help me on my actual exam date when I don't know how to find a solution to a question. Besides I'm sure people on here don't mind answering any queries I might have about certain questions (I hope) :colondollar:

And for your information, I'm not struggling with AS Maths at all; how can you state something so boldly without valid evidence? I may have asked about this particular question however the rest of the paper went fine giving quite a respectable mark.

Methinks I should stop feeding the troll now.

(edited 13 years ago)

Reply 16

BieberFan

Original post by Dededex

I'm perfectly fine with that but when you go to talk about Oxbridge maths, I find that it is insulting to anyone who has studied there in the past. There's almost nothing to understand in C1 AT ALL. You couldn't answer most of the questions you've posted, which are extremely basic.

All I'm saying is that you should not get your hopes up about oxbridge. I didn't apply to Oxbridge for maths because I knew I wasn't good enough. I found C1-C4 VERY straight forward. Did not need any help at all. You're struggling with C1 and C2 more than I struggled with STEP III ffs.

Maths isn't for you by the looks of things. Apply for something else and come down to Earth before you make a massive mistake.

What did you get in the SMC, that'll settle it. If you didn't get at least 75 marks then you do not have the right to argue against what I have said.

Reply 17

electriic_ink

Original post by BieberFan

On the contrary, these sorts of unis like people who ask questions when they're stuck. There's nothing worse than complacency.

Reply 18

BieberFan

Original post by electriic_ink

On the contrary, these sorts of unis like people who ask questions when they're stuck. There's nothing worse than complacency.

I said that there was nothing wrong with asking questions why. My problem occurs when he's struggling with such simple concepts. They will not expect him to be struggling with C1 or C2. Can you imagine what would happen at an interview (if he even got one)? It would be the most awkward thing for him to go through since those questions are very tough. Do you seriously think that anyone who struggles with C1/C2 at this stage of the AS year can cope with the Oxford admissions test or STEP in a under a year/by the summer of the year after next? I thought not.