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## Weekly Maths Challenge

### Seven Day Maths

Challenge 138: What's the point?

The curve with equation y = x2 – 2x – 3 , where b and c are positive real numbers, crosses the x-axis at A and B, and the y-axis at C.

If you draw the circle that goes through all the points A, B and C, what are the co-ordinates of the other point where it crosses one of the axes?

What about the curve with equation y = x2 – x – 3? Or y = x2 – 3x – 3?

Can you generalise for curves of the form y = x2 – bx – c, where b and c are positive real numbers?

Mathematics is a subject where you learn best by tackling problems. Every week, a new problem will be posted here for you to pit your wits against.

We invite you to have a go at solving it. If you get stuck, keep trying, and do go away and come back later – you will often find that you have a better idea on your second, third or even fourth attempt. If you have solved the problem, you can send your solutions to weeklymaths@kcl.ac.uk. You are welcome to either scan in written work, or to type your solutions. If you are emailing for the first time, please let us know what year you are currently in and what school you are at.

Past problems can be accessed below, and we welcome submissions of solutions for those too.

Follow us on Twitter here: @sevendaymaths, so that you never miss a new problem being posted!

Good luck!

#### Recent Challenges

Weekly Challenge 137

Weekly Challenge 136

Weekly Challenge 135

Weekly Challenge 134

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Weekly Challenge 102

Weekly Challenge 101

#### Older Challenges

Problems 81-100

Problems 61-80

Problems 41-60

Problems 21-40

Problems 1-20
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