Quadratic Inequalities (Edexcel A Level Maths) : Revision Note
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Quadratic Inequalities
Quadratic inequalities
Similar to quadratic equations quadratic inequalities just mean there is a range of values that satisfy the solution
Sketching a quadratic graph is essential
Can involve the discriminant or applications in mechanics and statistic

How do I solve quadratic inequalities?
STEP 1: Rearrange the inequality into quadratic form with a positive squared term
ax2 + bx + c > 0 (>, <, ≤ or ≥)
STEP 2: Find the roots of the quadratic equation
Solve ax2 + bx + c = 0 to get x1 and x2 where x1 < x2
STEP 3: Sketch a graph of the quadratic and label the roots
As the squared term is positive it will be "U" shaped
STEP 4: Identify the region that satisfies the inequality
For ax2 + bx + c > 0 you want the region above the x-axis
The solution is x < x1 or x > x2
For ax2 + bx + c < 0 you want the region below the x-axis
The solution is x > x1 and x < x2
This is more commonly written as x1 < x < x2
avoid multiplying or dividing by a negative number
if unavoidable, “flip” the inequality sign so < → >, ≥ → ≤, etc
avoid multiplying or dividing by a variable (x) that could be negative
(multiplying or dividing by x2 guarantees positivity (unless x could be 0) but this can create extra, invalid solutions)
do rearrange to make the x2 term positiveBe careful:

Solving quadratic inequalities on a calculator
Be aware of unconventional ways calculators can display an answer
eg 8 > x > 2 rather than 2 < x < 8

Examiner Tips and Tricks
A calculator can be super-efficient but some marks are for method.
Use your judgement:
is it a “show that” or “prove” question?
how many marks?
how long is the question?
Worked Example

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