AQA A Level Maths: Pure复习笔记2.2.2 Discriminants

What is a discriminant?

• The discriminant is the part of the quadratic formula that is under the square root sign
• It is sometimes denoted by the Greek letter  (capital delta)

How does the discriminant affect graphs and roots?

There are three options for the outcome of the discriminant:

• If >0  the quadratic crosses the x-axis twice meaning there are two distinct real roots
• If  =0  the quadratic touches the x-axis once meaning there is one real root (also called repeated roots)
• If  <0  the quadratic does not cross the x-axis meaning there are no real roots

Discriminant and inequalities

• You need to be able to set up and solve equations and inequalities (often quadratic) arising from the discriminant
• Sketch the quadratic and decide whether you're looking above or below zero to write your solutions correctly

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