M4.9.5 For the adult
The quadratic formula
x² + 4x + 1 = 0 does not factorise with whole numbers. Can I still solve it every time?
What this chapter teaches
The quadratic formula solves any equation ax² + bx + c = 0. The number b² − 4ac, the discriminant, tells how many solutions there are: two if it is above 0, one if it is 0, none if it is below 0. An area problem becomes a quadratic equation, and a negative answer for a length is dropped.
Three questions to ask
There is no one right wording. Listen for the idea.
- What are a, b and c in 2x² − 5x + 3 = 0?
- What does it mean when b² − 4ac is below 0?
- Why is a negative answer thrown away in an area problem?
After the chapter, the learner can
- Solve any quadratic equation with the formula
- Use b² − 4ac to say how many solutions there are
- Form and solve a quadratic from an area problem
What they copy into their notebook
Read off a, b and c with their signs. Work out b² − 4ac first. Then x = (−b ± √(b² − 4ac)) ÷ (2a). Above 0: two answers. At 0: one. Below 0: no real answer.