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tmua.me Extreme Set C Paper 1 · Q9

Paper 1TrigonometryAlgebra

For a real constant kk, the polynomial

p(t)=t3−kt2+(k−1)t+k32p(t)=t^3-kt^2+(k-1)t+\frac{k}{32}

has sin⁡θ\sin\theta and cos⁡θ\cos\theta as roots, where 0<θ<π40<\theta<\dfrac\pi4.

What is the value of kk?

A78\dfrac78
B98\dfrac98
C11
D54\dfrac54
E1+22\dfrac{1+\sqrt2}{2}
F94\dfrac94

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