x Turn on thread page Beta
 You are Here: Home >< Maths

# Find a cubic equation from quartic watch

1. I am stuck on the last part of a question. I correctly found the equation of the quartic which is . And the rootsare: . I don't know if this helps but the roots were stated as .

The last part of the question asks:

By making a suitable substitution y=x-k, for a suitable value of k, find a cubic equation with integer coefficients which has roots .

So I compared like this:

Old roots >>>>> New roots to find
>>>>>

>>>>>

>>>>>

So it looks like adding 2 to LHS gives you RHS. ie old root + 2 = new root.

So the cubic rots are: ??? Is that correct?

But if so, would it not be y = x + 2?

So I am confused about that.

If I am correct, then can I work out the new equation like this:

2. (Original post by acomber)
I am stuck on the last part of a question. I correctly found the equation of the quartic which is . And the rootsare: . I don't know if this helps but the roots were stated as .

The last part of the question asks:

By making a suitable substitution y=x-k, for a suitable value of k, find a cubic equation with integer coefficients which has roots .

So I compared like this:

Old roots >>>>> New roots to find
>>>>>

>>>>>

>>>>>

So it looks like adding 2 to LHS gives you RHS. ie old root + 2 = new root.

So the cubic rots are: ??? Is that correct?

But if so, would it not be y = x + 2?

So I am confused about that.

If I am correct, then can I work out the new equation like this:

add 2alpha to all the roots
3. (Original post by acomber)
... the roots were stated as .

The last part of the question asks:

By making a suitable substitution y=x-k, for a suitable value of k, find a cubic equation with integer coefficients which has roots .
What do you get if you subtract from each of ?

Turn on thread page Beta
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: December 4, 2014
Today on TSR

### Happy St Patrick's day!

How are you celebrating?

### Stay at sixth form or go to college?

Discussions on TSR

• Latest
Poll
Useful resources

## Make your revision easier

### 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

Can you help? Study help unanswered threads

## Groups associated with this forum:

View associated groups
Discussions on TSR

• Latest

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE