A Maths question

Find the largest positive value of k for which the equation 2^x - 4^(x - 4k) =0 has real roots. Ans: 1/8

Hi,

I feel that something is wrong with this question.

If we solve the equation, we obtain the solution x = 8k.

Thus there will be a real root regardless of k.

Thanks.

Cheers,
Wen Shih

Hi,

I suppose the equation should be 2x² - 4(x – 4k) = 0 ?

Deleted.

yeah i had x=8k as well .. thanks

Hi,

I feel that something is wrong with this question.

If we solve the equation, we obtain the solution x = 8k.

Thus there will be a real root regardless of k.

Thanks.

Cheers,
Wen Shih

By Subtituting x = 1, 2, 3 .... into x = 8k, the values of k become larger and larger.

The question requires us to find the largest positive value of k.

For k to be positive, x must be positive ie x > 0,

When x > 0, 8k > 0, k > 0.

Hence, the largest possible value of k will be k = infinity for one real root case

(not k = 1/8 as given by TS).

Hi,

The problem is ill-posed in the first place :P

Cheers,
Wen Shih

Hi Mr Wee,

I concur with you.

Regards.

PS : I saw the newly published 5-years GCE "N" level Additional Mathematics

(NA) TYS by Dyna at Big Bookshop a few days ago to which Mikethm, you

and me were discussing about the possibility of publication of the TYS last

year as there are only a small number of "N" level students taking "N" level

AMaths. I ponder whether Dyna can make profit from this TYS.

Hi,

I believe Dyna will monopolise this small market, so that is good enough already :)

Cheers,
Wen Shih