2022 SJI P1 Q3

2022 SJI P1 Q3

IB Year 5 | Grade 11
7 marks

Consider the cubic function \(\mathrm{f}(x)=-3x^3+8x^2-9x+10\), for \(x\in\mathbb R\).

  1. Show that \(x=2\) is a root of \(\mathrm{f}(x)=0\).[1]
  2. Express \(\mathrm{f}(x)\) as a product of two factors.[3]
  3. Hence, show that there are exactly two real solutions for the equation \[-3y^6+8y^4-9y^2+10=0.\][3]

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Answer:(a) Shown (b) \((x-2)(-3x^2+2x-5)\) (c) \(y=\pm\sqrt2\), exactly two real solutions.

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