Homework Help

The coefficient of x^2 in the expansion of (k+(1/3)x)^5 is 30. Find the value of the...

user profile pic

saj-94 | (Level 1) Salutatorian

Posted September 10, 2013 at 9:27 AM via web

dislike 1 like

The coefficient of x^2 in the expansion of (k+(1/3)x)^5 is 30. Find the value of the constant k.

1 Answer | Add Yours

user profile pic

jeew-m | College Teacher | (Level 1) Educator Emeritus

Posted September 10, 2013 at 9:32 AM (Answer #1)

dislike -1 like

`(k+1/3x)^5`

Using binomial theorem;

`(k+(1/3)x) = sum_(r=0)^5^5C_r (x/3)^r k^(5-r)`

The coefficient of `x^2` can be obtained when r = 2.

Coefficient of `x^2 = ^5C_2 (1/3)^2 k^5-2 = 30`

`(10/9) xx k^3 = 30`

`K^3 = 27`

`k= 3`

So the value of k is 3.

Sources:

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes