The discriminant, a line and a curve
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The teaching part (1 min) is free to watch. A free account opens the whole lecture: 5 worked examples, 5 practice questions, 1 real past-paper question with the answer explained, the mistakes that lose marks, the full-marks tip, a one-card summary and a quick quiz.
What this lecture covers
- Count the roots without solving
- The discriminant
Read the transcript of the teaching part
Last time
Before we start: last time, in Solving quadratics and completing the square, you learned these points. Here they are again on one card. Keep them in mind, because today builds on them.
Count the roots without solving
A quadratic can cut the x axis twice, touch it once, or miss it completely. Do you need to solve the equation to know which? No. One number, found in seconds, tells you. It is called the discriminant.
The discriminant
For a x squared plus b x plus c equals zero, the discriminant is b squared minus four a c. It is the part under the root in the formula. If D is positive, there are two different real roots. The curve cuts the x axis twice. If D is zero, the two roots are equal. The curve just touches the x axis. If D is negative, there are no real roots. The curve never reaches the x axis.
How often it comes up
How often Cambridge has asked each part, counted by ExamYard from every past paper in its question bank: Discriminant and intersections · Discriminant and tangency.
The whole chapter: Quadratics.
Chapter 1.1: Quadratics
- Solving quadratics and completing the square 5 min
- The discriminant, a line and a curve 6 min
Also for A Level Maths 9709 Paper 1
Which topics come up most in A Level Maths 9709 Paper 1 past papers, counted from every paper since 2004.