You are Here: Home >< Maths

# Roots of Cubics watch

1. x^3 - 5x + 3 = 0 (I'm going to call the roots A, B, and Y as latex isn't working)

Find A + B + Y (0)

Find A^2 + B^2 + Y^2 (10)

Find A^3 + B^3 + Y^3

I tried multiplying the first and second parts of the question together to see if it simplified down to A^3 + B^3 + Y^3 + some other stuff, but I couldn't get it in terms of Sigma(A), Sigma(AB) and ABY.

I know that Sigma(A^2) = [Sigma(A)]^2 - 2(Sigma(AB))
Is there a similar formula for Sigma(A^3) that I am supposed to use?
x^3 - 5x + 3 = 0 (I'm going to call the roots A, B, and Y as latex isn't working)

Find A + B + Y (0)

Find A^2 + B^2 + Y^2 (10)

Find A^3 + B^3 + Y^3

I tried multiplying the first and second parts of the question together to see if it simplified down to A^3 + B^3 + Y^3 + some other stuff, but I couldn't get it in terms of Sigma(A), Sigma(AB) and ABY.

I know that Sigma(A^2) = [Sigma(A)]^2 - 2(Sigma(AB))
Is there a similar formula for Sigma(A^3) that I am supposed to use?
Whilst there is a formula, it's not necessary.

Since A is a root of your polynomial x^3 - 5x + 3 = 0, then

A^3 - 5A + 3=0

Similarly for B,C.

Add the three equations, and ....
3. (Original post by ghostwalker)
Whilst there is a formula, it's not necessary.

Since A is a root of your polynomial x^3 - 5x + 3 = 0, then

A^3 - 5A + 3=0

Similarly for B,C.

Add the three equations, and ....
Never thought of trying that, thanks!
Never thought of trying that, thanks!
np.

As an extension you might like to consider what the sum of the fourth powers is.

Route to answer in the spoiler

Spoiler:
Show

Multiply the original polynomial by x, and proceed as for the cubes.

And the fifth,...

until you're bored.

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: November 17, 2013
Today on TSR

### Cambridge interviews

Find out who is getting invitations

### University open days

• University of Roehampton
Sat, 17 Nov '18
• Edge Hill University
Faculty of Health and Social Care Undergraduate
Sat, 17 Nov '18
• Bournemouth University
Sat, 17 Nov '18
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