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Daniel J Smith Custom TMUA Set A Paper 1 · Q7

Paper 1Functions & graphsAlgebra

Let a>0a>0 and kk be real numbers

Consider the cubic

g(x)=x3−3ax+kg(x)=x^3-3ax+k

For which complete range of values of kk does the equation g(x)=0g(x)=0 have three distinct real roots?

A−2a3/2<k<2a3/2-2a^{3/2}<k<2a^{3/2}
B−2a3/2≤k≤2a3/2-2a^{3/2}\leq k\leq2a^{3/2}
C−a3/2<k<a3/2-a^{3/2}<k<a^{3/2}
D−2a3<k<2a3-2a^3<k<2a^3
Ek<−2a3/2k<-2a^{3/2} or k>2a3/2k>2a^{3/2}
F−2a3/2<k≤2a3/2-2a^{3/2}<k\leq2a^{3/2}
G−2a3/2≤k<2a3/2-2a^{3/2}\leq k<2a^{3/2}

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