CAIE A-Level Mathematics AS 1.1.2 Quadratic Discriminant Questions
Practise solving and interpreting quadratic functions and equations within the AS mathematics syllabus.
- Syllabus
- 2028–2030
- Course
- Mathematics 9709
- Level
- AS
Exam points
- solve quadratic equations using appropriate methods
- analyse roots, discriminants and intersections
- interpret quadratic functions in context
CAIE A-Level Mathematics AS 1.1.2 Quadratic Discriminant Questions question 1
[Maximum number: 3]
The function f is defined, for x∈R, by f:x↦x2+ax+b, where a and b are constants.
Show that if the equation f(x+a)=a has no real roots then a2<4(b−a).
(x+a)2+a(x+a)+b=a.
M1*
Use the discriminant for the resulting quadratic:
9a2−4(2a2+b−a)<0.
DM1
Hence
a2<4(b−a).
A1 AG
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