Maths Times Infinity > Topics > Quadratics
Quadratics
A quadratic is a special case of a polynomial. A polynomial is an expression involving a sum of powers of a variable. For example, a3+5a4 or 7y+11. 7y+11 can be thought of as 7y1 + 11y0. Now, a quadratic is a polynomial where the highest power is a 2. Like p2-4p+9 or 8-25b2.
A general formula is ax2+bx+c where x is the variable and a,b and c are constants. It's important that a isn't zero or else it wouldn't be a quadratic, it would then be a linear function.
Solving Quadratics
Let's say you know that x2-5x+6=0. What could x be? What's an efficient way to find out? Well, it turns out that x2-5x+6=(x-2)(x-3) which you can check for yourself. So it factorises. Now we know that (x-2)(x-3)=0. Two numbers multiplying to give 0. Hang on, that means one of the two numbers has to be zero! You can't multiply two non-zero numbers and get zero. So either x-2=0 or x-3=0. Solving these two equations tells us that either x=2 or x=3. There's no other way it could possibly work!
This is one way we can solve quadratic equations - by factorising them. Another way is by completing the square.