(k+x)(1+3x)^8 k is a constant,when coefficient of x=0 find the value of k

Question

anonymous · Answer

Please reformulate your question. I don't get it.

kc_kennylau · Answer

When constant in (1+3x)^8 is obviously 1, and the coefficient of x in (1+3x)^8 is 24x (ask me if you don't know how I got this)

kc_kennylau · Answer

Therefore the coefficient of x in (k+x)(1+3x)^8 is... hmm... I think you know how to calculate it now don't you

anonymous · Answer

Just plug in x=0 in the equation.

anonymous · Answer

Can you do that?

kc_kennylau · Answer

And @JoelSjogren the question is comprehensible enough

anonymous · Answer

I disagree but I get it thanks to you.

kc_kennylau · Answer

Oh okay then

anonymous · Answer

Isn't x going to be 0 if its coefficient is 0x = 0.

anonymous · Answer

@kc_kennylau

ganeshie8 · Answer

x=0 wud make all other terms also 0, except the constant term.. 
so....

anonymous · Answer

the value of k is - 1/24 ?

kc_kennylau · Answer

exactly

kc_kennylau · Answer

I think so

ganeshie8 · Answer

(k+x)(3x+1)^8

(k+x)[(8 0)(3x)^8*1^0 + (8 1) (3x)^7 * 1^1 + .... (8 7)(3x)^1 1^7 + (8 8) (3x)^0 1^8 ]

kc_kennylau · Answer

@ganeshie8 please don't expand it fully...

ganeshie8 · Answer

you want to consider last two terms @AnImEfReaK 
those give u coefficients of x

ganeshie8 · Answer

??

anonymous · Answer

Yes i know now.

anonymous · Answer

the value of K? @ganeshie8

ganeshie8 · Answer

-1/24 is right

anonymous · Answer

thanks..

anonymous · Answer

As a side note, you can also do this using calculus. Let the expression be y and equate the constant term of y' with 0.

kc_kennylau · Answer

Wow I never thought of it

anonymous · Answer

@JoelSjogren  I mean whats the use of taking the derivative?

anonymous · Answer

$$y = (k + x)(1 + 3x)^8$$
By the product rule and the chain rule,
$$y \prime = 1(1 + 3x)^8 + (k + 3x)8(1 + 3x)^7 3$$
We want the constant term, so we look for the value when x = 0:
$$y' = 1 + k*24$$
This is 0. Solving for k gives k = -1/24

anonymous · Answer

Boblovesmath, it's beautiful. Other than that, I don't know the use of it.

anonymous · Answer

@JoelSjogren  I know but I mean why did you take the slope of the tangent line at that point?  Why did you do the derivative?

anonymous · Answer

The slope of the tangent line is the coefficient of x.

anonymous · Answer

@JoelSjogren  Ohhhh!!!!! I got it now thanks!!! Thanks for putting it forward, I really appreciate it.

anonymous · Answer

No problem!

loser66 · Answer

@JoelSjogren  Beautiful job!!! never know this way. Thanks for posting.