Quadratic Equations Summary

GCSE Maths

Quadratic equations take the form ax² + bx + c = 0
e.g. 3x² + 5x -10 = 0

There are often two solutions to a quadratic equation, and they are frequently negative.

When b=0, the equations are: ax² + c = 0.
These can just be manipulated using basic algebra.

When c=0, the equations are: ax² + bx = 0
These can just be factorised into x (ax + b) = 0 and each term solved.

Any quadratic equation can be solved by plugging its numbers into:
Quadratic Formula solution: x = (-b +/- root(b^2 - 4ac))/2a

Quadratic equations can often be factorised.
e.g. x² + 21x + 110 = 0
x² + 10x + 11x + 110 = 0
x (x + 10) + 11 (x + 10) = 0
(x + 10)(x + 11) = 0
Solutions: x=-10 and x=-11


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