CAIE A-Level Mathematics AS 1.1.3 Quadratic Equations Questions
Practise solving and interpreting simultaneous equations and inequalities within the AS mathematics syllabus.
- Syllabus
- 2028–2030
- Course
- Mathematics 9709
- Level
- AS
Exam points
- solve simultaneous equations algebraically and graphically
- solve linear and quadratic inequalities
- interpret solution sets and intersections
CAIE A-Level Mathematics AS 1.1.3 Quadratic Equations 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.
It is given instead that a=5 and that the roots of the equation f(x)=0 are k and -2 k, where k is a constant.
Find the values of b and k.
(x−k)(x+2k)≡x2+5x+b.
Comparing coefficients of x:
k=5.b=−2k2=−50.
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