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

# Interesting Misprint Question watch

1. The quadratic x2+4x-3=0 was misprinted as x2+4x-3=0 on a worksheet of mine. I have now been set it for homework after expressing interest in it.
Can anyone offer me advice on solving it algebraically, graphically by plotting y=4x and y=3-x2 I can see there are two solutions.
2. (Original post by ThreePoint14159)
The quadratic x2+4x-3=0 was misprinted as x2+4x-3=0 on a worksheet of mine. I have now been set it for homework after expressing interest in it.
Can anyone offer me advice on solving it algebraically, graphically by plotting y=4x and y=3-x2 I can see there are two solutions.
You are going to need to use the graphical method you used or a numerical method.
3. The iterative formula:

converges to the positive root fairly quickly.

The iterative formula:

converges to the negative root incredibly slowly.

Newton Raphson finds either root so long as you start near enough:

4. (Original post by Mr M)
The iterative formula:

converges to the positive root fairly quickly.

The iterative formula:

converges to the negative root incredibly slowly.
Great! Thanks very much.
5. (Original post by ThreePoint14159)
Great! Thanks very much.
You are welcome. Just checking you know how to use an iterative formula?
6. (Original post by Mr M)
You are welcome. Just checking you know how to use an iterative formula?
I do, incidentally just been doing Newton-Raphson in FP1
I had considered doing numerical methods, just took me a while to differentiate 4x for Newton Raphson but I'm sorted now!
7. (Original post by ThreePoint14159)
I do, incidentally just been doing Newton-Raphson in FP1
I had considered doing numerical methods, just took me a while to differentiate 4x for Newton Raphson but I'm sorted now!
Good.
8. Here's a nice way to prove there are no integral solutions:

(*) .

Case 1: If x<-1 then LHS<0 but RHS is always positive, hence no solutions.

Case 2: If x=-1 then 2=1/2, contradiction.

Case 3: If x=0 then 3=1, contradiction.

Case 4: If x is at least 1 then the RHS has at least one factor of 4. Therefore taking mod 4 of both sides yields , which is absurd since 3 isn't a quadratic residue modulo 4.

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: October 8, 2013
Today on TSR

### Which business legend are you?

We have the answer...

### University open days

• University of Bradford
Wed, 21 Nov '18
• Buckinghamshire New University
Wed, 21 Nov '18
• Heriot-Watt University
Wed, 21 Nov '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