Key learning point(s): Nature of roots
This is determined by the Discriminant (D), which is b^2-4ac, and is also derived from the general formula for Quadratic formulas.
There are three cases:
- When D=0, roots are real and distinct - Graph intersects x-axis twice (Example: x = -2 or 4)
- When D > 0, roots are real and equal - Graph's tangent for turning point is x-axis (Example: x=2)
- When D < 0, roots are imaginary or complex - Graph does not cut x-axis (Example: x=3+4i, x=3+4sqrt-1)
∴ When D ≥ 0, roots are real.
• When considering whether a variable will result in a positive Discriminant, consider signage! (Example: a^2)
-seen in Pract. 8 (page 157)