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mathematics UK Year 12 Mathematics (AS) Quadratic inequalities
 
Quadratic inequalities
 

Quadratic inequality





1. Leading coefficient a > 0 (function facing up)
1.1. D > 0 (the function has two real zeros)
1.2. D = 0 (the function has a repeated real zero)
1.3. D < 0 (function has no real zeros)
2. Leading coefficient a < 0 (downward facing function)
2.1. D > 0 (the function has two real zeros)
2.2. D = 0 (function has a repeated real zero)
2.3. D < 0 (function has no real zeros)
3. Forum

A quadratic inequality can have the following forms:










The solutions of a quadratic inequality are obtained by finding where the corresponding quadratic function is positive, negative or equal to zero.


Leading coefficient a > 0 (function facing up)



D > 0 (the function has two real zeros)



The function has the form:





D = 0 (the function has a repeated real zero)



The function has the form:





D < 0 (function has no real zeros)



The function has the form:





Leading coefficient a < 0 (downward facing function)



D > 0 (the function has two real zeros)



The function has the form:





D = 0 (function has a repeated real zero)



The function takes the form:





D < 0 (function has no real zeros)



The function takes the form:





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