Cofficient

i.shaikh3 said:
pleas can you help. thank you
View attachment 24932
Click to expand...
I can't tell what sort of help you need, unless you show some work or ask a specific question.

Presumably you know the binomial expansion; you might either write the whole thing out, or ,more efficiently, use the formula for the nth term to write the term with x^4. Then you can set that coefficient (an expression in terms of a) equal to 60, and solve.
 
Subhotosh Khan said:
Do you know the binomial expansion of (a + b)n?

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:


Please share your work/thoughts about this problem.
Click to expand...
thank you.
I myself a doctor. Was posting on behalf of my son. Will ask him to study binomial equation. However, it seems only way to solve coefficient for a particular number is (nCr) a ^(n-r) b^r. I guess they just have to remember the equation in exams. thank you
 
Dr.Peterson said:
I can't tell what sort of help you need, unless you show some work or ask a specific question.

Presumably you know the binomial expansion; you might either write the whole thing out, or ,more efficiently, use the formula for the nth term to write the term with x^4. Then you can set that coefficient (an expression in terms of a) equal to 60, and solve.
Click to expand...
thank you sir
 
i.shaikh3 said:
thank you.
I myself a doctor. Was posting on behalf of my son. Will ask him to study binomial equation. However, it seems only way to solve coefficient for a particular number is (nCr) a ^(n-r) b^r. I guess they just have to remember the equation in exams. thank you
Click to expand...
Correct>

This is a very important equation that will come up many other types of problems. It will be very useful to "cram" this expression of binomial theorem.
 
i.shaikh3 said:
thank you.
I myself a doctor. Was posting on behalf of my son. Will ask him to study binomial equation. However, it seems only way to solve coefficient for a particular number is (nCr) a ^(n-r) b^r. I guess they just have to remember the equation in exams. thank you
Click to expand...
Of course, the missing information is, what is your son learning? What course is he taking?

If he has not been taught this formula in class, and the assignment was for that class, then presumably they expect him to solve it a somewhat different way. If he can just expand (2x+a)^6, even just by writing it as (2x+a)(2x+a)(2x+a)(2x+a)(2x+a)(2x+a), or as (2x+a)^2(2x+a)^2(2x+a)^2, then he should do that. This is what I meant by "you might ... write the whole thing out".

But, yes, the binomial formula will sooner or later be important to learn.
 
Dr.Peterson said:
Of course, the missing information is, what is your son learning? What course is he taking?

If he has not been taught this formula in class, and the assignment was for that class, then presumably they expect him to solve it a somewhat different way. If he can just expand (2x+a)^6, even just by writing it as (2x+a)(2x+a)(2x+a)(2x+a)(2x+a)(2x+a), or as (2x+a)^2(2x+a)^2(2x+a)^2, then he should do that. This is what I meant by "you might ... write the whole thing out".

But, yes, the binomial formula will sooner or later be important to learn.
Click to expand...
Thank you. He is actually in year 11, called GCSE in England, not sure what is that level in US. You are right, it depends on what he has been taught. Sadly due to lockdown no/minimal teaching since 6 months, these little guys are just solving old questions, pretty much self study. Anyways, point taken.
 
i.shaikh3 said:
Thank you. He is actually in year 11, called GCSE in England, not sure what is that level in US. You are right, it depends on what he has been taught. Sadly due to lockdown no/minimal teaching since 6 months, these little guys are just solving old questions, pretty much self study. Anyways, point taken.
Click to expand...
Although it has been forty since I lived is Manchester, I did at one time know about the GCSE.
A year 11 student should know that \({(2x + a)^{^6}} =\displaystyle \sum\limits_{k = 0}^6 { \dbinom{6}{k} {{(2x)}^{6 - k}}{a^k}} \)
Here \(k=2\) so \((2x)^4a^2\). Now what is \(\dbinom{6}{2}=~?\) solve for \(a\).
If you post it, we will check it.
 
pka said:
(62)
Click to expand...
Hello, I am answering on behalf of my Dad, the answer to your question is 15, as I can work out 6!/(2!4!) will be 30/2 =15. To continue, I would take 24 as 16, and leave x4. Then the expression would look like 16x4a2*15. To simplify the expression would be 240a2x4. In the question, we are given the coefficient of the x4 is 60.

The equation for this could be 240a2x4 = 60x4.
Canceling out the x4. The equation would be 240a2 = 60.
Divide both sides by 240. a2 = 60/240
To simplify the equation is. a2 = 1/4
The square root both sides. a = ± 1/2 ...........................................edited

Thank you, for this new method of answering this question.
 
Last edited by a moderator:
Farrah said:
Hello, I am answering on behalf of my Dad, the answer to your question is 15, as I can work out 6!/(2!4!) will be 30/2 =15. To continue, I would take 24 as 16, and leave x4. Then the expression would look like 16x4a2*15. To simplify the expression would be 240a2x4. In the question, we are given the coefficient of the x4 is 60.

The equation for this could be 240a2x4 = 60x4.
Canceling out the x4. The equation would be 240a2 = 60.
Divide both sides by 240. a2 = 60/240
To simplify the equation is. a2 = 1/4
The square root both sides. a = 1/2.

Thank you, for this new method of answering this question.
Click to expand...
Remember - you were asked provide "possible values" of a - plural.

So your answer should contain multiple values of a.
 
Yes sorry, I had forgotten to add the negative, -1/2 root, and positive 1/2 root of 1/4 in my reply.
 
You must log in or register to reply here.
Top