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

# Help me with this question please watch

1. I just need to know what to do :/

The cubic equation x^3 + Ax^2 + Bx + 15 = 0

Where A and B = real numbers

Root = x = 1+2j

Q. Find the value of the real root and the values of A and B

I did something weird and got A as 2j and B as 4, but I heard the correct answer is 1 and -1, can someone explain the process? Thanks
2. If the coefficient of a polynomial are real then any complex roots must occur in conjugate pairs. This means you can write down a second root. You now have two values you can put in the equation for x and this will enable you to obtain a pair of simultaneous equations in A and B.
3. I know the second root is x = 1-2j, but I have no idea what to do from there :/
4. if one root is 1+2j then another is 1-2j due to complex conjugates. Therefore factors will be x-1-2j and x-1+2j . Multiply them together and do a long division to find the third factor.
5. (Original post by superfoggy)
if one root is 1+2j then another is 1-2j due to complex conjugates. Therefore factors will be x-1-2j and x-1+2j . Multiply them together and do a long division to find the third factor.
I did exactly that then I ended up with x^2 - 2x + (a real number i forgot which)
6. yes youl need to do what mr m said to find a and b
then do the long division.

x^2 - 2x + 5 i believe
7. (Original post by superfoggy)
yes youl need to do what mr m said to find a and b
then do the long division.

x^2 - 2x + 5 i believe
So x^2 - 2x + 5 is the real root?

How do I find the value of A and B?

Thanks
8. (Original post by superfoggy)
yes youl need to do what mr m said to find a and b
then do the long division.

x^2 - 2x + 5 i believe
So x^2 - 2x + 5 is the real root?

How do I find the value of A and B?

Thanks
9. I did tell you one method but you ignored it. A quadratic expression cannot be a real root.

do i need to factorise?
11. Having got this far do this:

Expand the brackets, collect like terms and equate coefficients (match up each term on the left hand side and the right hand side).
12. (Original post by Mr M)
Having got this far do this:

Expand the brackets, collect like terms and equate coefficients (match up each term on the left hand side and the right hand side).
ahh i swear to god i did exactly this in the test

i forgot the = 0 at the end of the first equation
13. (Original post by Mr M)
Having got this far do this:

Expand the brackets, collect like terms and equate coefficients (match up each term on the left hand side and the right hand side).

14. can someone tell me what to do from here?
15. (Original post by YouWillNotKnow)
can someone tell me what to do from here?
Collect like terms? Look at the numbers on the end and figure out the value of k?
16. imo, the simplest way to do these is if you have a POLYNOMIAL x^3 + ax^2 +bx +c =0, with roots d, e and f, then c= -def, b=de+ef+df, and a= -(d+e+f)
17. (Original post by Mc^3)
imo, the simplest way to do these is if you have a quadratic x^3 + ax^2 +bx +c =0, with roots d, e and f, then c= -def, b=de+ef+df, and a= -(d+e+f)
Are you sure?
18. (Original post by Mr M)
Are you sure?
polynomial, you know what i mean. i think the method's right...
19. (Original post by Mr M)
Collect like terms? Look at the numbers on the end and figure out the value of k?
there are no like terms though :/
20. (Original post by YouWillNotKnow)
Look at the ends.

-5k = ?

So what is k?

You say there are no like terms but I can see and terms ...

You are struggling badly here. I think you may need to see your teacher for some help.

Turn on thread page Beta

### Related university courses

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: October 1, 2010
The home of Results and Clearing

### 2,852

people online now

### 1,567,000

students helped last year
Today on TSR

### University open days

1. London Metropolitan University
Sat, 18 Aug '18
2. Edge Hill University
Sat, 18 Aug '18
3. Bournemouth University
Clearing Open Day Undergraduate
Sat, 18 Aug '18
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

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