2026 GESS P2 Q5

2026 GESS P2 Q5

Secondary 4
12 marks
    1. Show that \(3x+2\) is a factor of \(f(x)=6x^3-8x^2+x+6\) and hence factorise \(6x^3-8x^2+x+6\) completely.[5]
    2. Determine the number of real roots of the equation \(f(x)=0\), justifying your answer.[2]
    1. Solve the following equation \(4(3)^{2p}+(3)^p+5=8\).[3]
    2. Show that the real solution from part (b)(i) may be written in the form \(1-\log_a b\) where \(a\) and \(b\) are integers to be determined.[2]

Solution:

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Answer:(a)(i) \((3x+2)(2x^2-4x+3)\). (ii) One real root. (b)(i) \(p=-0.262\). (ii) \(a=3,b=4\).

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