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# How to do this C3 question? Tweet

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1. Re: How to do this C3 question?
I don't understand why the equation has no real roots? The equation, in this case, is below zero not the discriminant?
2. Re: How to do this C3 question?
(Original post by Fusionary)
I don't understand why the equation has no real roots? The equation, in this case, is below zero not the discriminant?
The question says for all values of

Notice the bolded part, that is very important here.

So when we write the equation as , then this means that is greater than zero for all values of . Hence it doesn't crosses the x-axis so it has no real roots.

For no real roots the discriminant is

Does it makes sense?
3. Re: How to do this C3 question?
Ahhhhh, I understand perfectly now, thank you very very much!
4. Re: How to do this C3 question?
I'm just wondering when you are working out the range of composite functions, do you use complete the square method or do you use discriminant method?
5. Re: How to do this C3 question?
(Original post by Fusionary)
I'm just wondering when you are working out the range of composite functions, do you use complete the square method or do you use discriminant method?
Do you mean for quadratics? The best way's to find the range of a quadratic are to either complete the square or to differentiate it. Both ways find the minimum/maximum point and you can find the range from there.
6. Re: How to do this C3 question?
(Original post by raheem94)
I have posted some working, if it doesn't makes sense tell me, so that i can explain it further.
hi could you help me with a question please.

jan 12 ocr c3 8iii

thanks a lot
7. Re: How to do this C3 question?
(Original post by Fusionary)
I'm just wondering when you are working out the range of composite functions, do you use complete the square method or do you use discriminant method?
These things come to your preference. Do the method in which you are most confident.
8. Re: How to do this C3 question?
(Original post by ugk4life)
hi could you help me with a question please.

jan 12 ocr c3 8iii

thanks a lot
I can't help unless you give me the question.

Post your question. I don't have the paper.
9. Re: How to do this C3 question?
The paper is here http://www.thestudentroom.co.uk/show...OCR%20Core%203
Would you be able to help with question 9 please? im really stuck.
10. Re: How to do this C3 question?
(Original post by raheem94)
I can't help unless you give me the question.

Post your question. I don't have the paper.
ok.

8) i) cos4x = 1-8sin^2(x)cos^2(x)

ii) Hence find the exact value of sin^2(pi/24)cos^2(pi/24). answer is (2-root3)/16.

iii) by expressing 2cos^2(2x)-8/3sin^2(x)cos^2(x) in terms of cos4x, find maximum value of 2cos^2(2x)-(8/3)sin^2(x)cos^2(x)

thanks
11. Re: How to do this C3 question?
This is how you do 8iii. Please could anyone help me on question 9?

cos4x= 2cos^2 2x -1
2cos^2 2x = cos4x +1

cos4x= 1-8sin^2 xcos^2 x
cos4x -1 = -8sin^2 xcos^2 x
(1/3)(cos4x-1) = -(8/3)sin^2 xcos^2 x

they wanted 2cos^2 2x - (8/3)sin^2 xcos^2 x

so: cos4x+1+(1/3)cos4x-(1/3)
(4/3)cos4x + (2/3)

Then replace cos4x by -1 to get (-2/3) and by 1 to get 2
12. Re: How to do this C3 question?
(Original post by ugk4life)
ok.

8) i) cos4x = 1-8sin^2(x)cos^2(x)

ii) Hence find the exact value of sin^2(pi/24)cos^2(pi/24). answer is (2-root3)/16.

iii) by expressing 2cos^2(2x)-8/3sin^2(x)cos^2(x) in terms of cos4x, find maximum value of 2cos^2(2x)-(8/3)sin^2(x)cos^2(x)

thanks

Remember,

13. Re: How to do this C3 question?
(Original post by drumdrum)
This is how you do 8iii. Please could anyone help me on question 9?

cos4x= 2cos^2 2x -1
2cos^2 2x = cos4x +1

cos4x= 1-8sin^2 xcos^2 x
cos4x -1 = -8sin^2 xcos^2 x
(1/3)(cos4x-1) = -(8/3)sin^2 xcos^2 x

they wanted 2cos^2 2x - (8/3)sin^2 xcos^2 x

so: cos4x+1+(1/3)cos4x-(1/3)
(4/3)cos4x + (2/3)

Then replace cos4x by -1 to get (-2/3) and by 1 to get 2

(Original post by raheem94)

Remember,

thanks a lot, just one question

how do you know that cos4x= 2cos^2 2x -1
14. Re: How to do this C3 question?
(Original post by ugk4life)
thanks a lot, just one question

how do you know that cos4x= 2cos^2 2x -1

Replace by
15. Re: How to do this C3 question?
no worries, i figured it is double angle
16. Re: How to do this C3 question?
(Original post by drumdrum)
The paper is here http://www.thestudentroom.co.uk/show...OCR%20Core%203
Would you be able to help with question 9 please? im really stuck.
On which part of question 9 do you need help?
17. Re: How to do this C3 question?
Because one of the cos2x identities is 2 cos^2(x) - 1
So cos4x will be 2cos^2 2x -1
18. Re: How to do this C3 question?
Last edited by Fusionary; 13-06-2012 at 16:35.
19. Re: How to do this C3 question?
(Original post by raheem94)
On which part of question 9 do you need help?
I have sorted part ii now, i just need help on 9i and 9iii

Thanks
20. Re: How to do this C3 question?
(Original post by drumdrum)
I have sorted part ii now, i just need help on 9i and 9iii

Thanks
9i,

Spoiler:
Show

Hope it makes sense