# How do I solve a quadratic equation by factorising?

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A quadratic equation is one that includes xas the highest power of x. Factorising is achieved in 3 steps. Let’s consider the example x2-3x-3=1

1) Put the equation into the form ax2+bx+c=0

x2-3x-4=0

2) Factorise

We need two numbers that

- add together to get -3

- Multiply together to get -4

-4x1=-4 and -4+1=-3

Thus, factorising gives (x-4)(x+1)=0

3) Solve the equation!

If two numbers are multiplied together to give 0, one of them must be 0. Thus:

x-4=0 and x=4

x+1=0 and x=-1

The equation has been solved

- This technique can be applied to finding the points of intersection on the x axis for a quadratic graph. For example, y=x2-3x-4. At the x axis, y=0 so you can work out x as above.

- Harder quadratic equations can also be solved by factorising. For example when a isn't 1.

2x2 + 7x + 3=0

Find two numbers that multiply to give 2x3 (6) and add to give 7. In this case, 6 and 1.

Split 7x into 6x +x

2x2 + 6x+x + 3=0

Factorise each part by taking out a common factor.

2x(x+3)+1(x + 3)=0

The sames as

(2x+1)(x+3)=0

thus x = -1/2 or x=-3

Practice questions

1. Solve by factorising

x2 + 6x + 8=0

x2 – 8x + 16 = 0

2. Find the points of intersection with the x axis for

y=x2 – 14x + 48

and sketch this function

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