2025 Beatty Sec 3 EOY Q1

2025 Beatty Sec 3 EOY Q1

Secondary 3
5 marks
  1. Express \(1-6x-2x^2\) in the form of \(p(x+q)^2+r\), where \(p\), \(q\) and \(r\) are constants.[2]
  2. Find the range of values of the constant \(k\) for which the equation \(1-6x-2x^2=kx+3\) does not have two distinct roots.[3]

Solution:

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Answer:(a) \(-2\left(x+\dfrac32\right)^2+\dfrac{11}{2}\); (b) \(-10\leq k\leq-2\).

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