Topic explanation

Standard explanation

x^2-6x+9=0 has D=0, repeated 3. x^2-3x+1=0 has D=5, two irrational reals. x^2+2x+5=0 has D=-16, non-real.

Key points

• sign of D
• D>0 two reals
• D=0 repeated
• keep the ideas separate
• The Three Cases: x^2-6x+9=0 has D=0, repeated 3. x^2-3x+1=0 has D=5, two irrational reals. x^2+2x+5=0 has D=-16, non-
• WHAT — THE THREE CASES: x^2-6x+9=0 has D=0, repeated 3. x^2-3x+1=0 has D=5, two irrational reals. x^2+2x+5=0 has D=-16, non-
• HOW — Use the idea: Identify what is given, select this topic's rule or evidence, apply it one step at a time, and check
• CORE UNDERSTANDING: x^2-6x+9=0 has D=0, repeated 3. x^2-3x+1=0 has D=5, two irrational reals. x^2+2x+5=0 has D=-16, non-

Labelled diagram