2024 ACS(BR) P2 Q3

2024 ACS(BR) P2 Q3

Secondary 4
7 marks
  1. Show that the roots of the equation \(ax^2+(3a+b)x+3b=0\) are real for all real values of \(a\) and \(b\).[3]
  2. Find the range of values of \(m\) for which the line \(y=mx-3\) will never cut the curve \(y^2=4x-6y-34\).[4]

Solution:

Solution locked

Sign in to view the step-by-step solution

Similar questions are unavailable for this question.
Answer:(a) Discriminant \((3a-b)^2\ge0\) for \(a\ne0\); the degenerate case also has real solutions. (b) \(m<-\dfrac25\) or \(m>\dfrac25\).

Need help? Join our JC Math tuition classes.

Learn more