2026 HGV P1 Q8

2026 HGV P1 Q8

Secondary 4
10 marks

It is given that \(\mathrm{f}(x)=2x^3+ax^2+x+b\).

  1. Find the value of \(a\) and of \(b\) for which \(2x^2+x-1\) is a factor of \(\mathrm{f}(x)\).[5]
  2. Solve the equation \(\mathrm{f}(x)=0\).[3]
  3. Hence solve \(\dfrac14y^3+\dfrac a4y^2+\dfrac12y+b=0\).[2]

Solution:

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Answer:(a) \(a=5\), \(b=-2\). (b) \(x=\dfrac12,-1,-2\). (c) \(y=1,-2,-4\).

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