You are Here: Home >< Maths

# Help, C2 (I'm posting all my questions here!) watch

Announcements
1. The coefficient of x^3 in the expansion of (2+x)(3-ax)^4 is 30.
Find the values of a.

I can't get the right answer. could someone show me their workings?
Ty
2. (Original post by [email protected])
The coefficient of x^3 in the expansion of (2+x)(3-ax)^4 is 30.
Find the values of a.

I can't get the right answer. could someone show me their workings?
Ty
On use of the binomial theorem, we find that the coefficient of x^3 is

-24a^3 + 54a^2

We equate that to 30 and solve!

-24a^3 + 54a^2 = 30
=> 24a^3 - 54a^2 + 30 = 0
=> 4a^3 - 9a^2 + 5 = 0
=> (a - 1)(4a^2 - 5a - 5) = 0
=> a = 1, (5/8) +/- root(105)/8

Euclid.

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: January 17, 2005
Today on TSR

### Four simple steps to get an A*

Here's all you have to do

Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams