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Official 2016 Paper 2 · Q14

Paper 2Algebra

Let f(x)=ax4+bx3+cx2+dx+ef(x)=ax^4+bx^3+cx^2+dx+e, where aa, bb, cc, dd, and ee are real numbers.

The equation f(x)=1f(x)=1 has pp distinct real solutions, the equation f(x)=2f(x)=2 has qq distinct real solutions, the equation f(x)=3f(x)=3 has rr distinct real solutions, and the equation f(x)=4f(x)=4 has ss distinct real solutions.

Which one of the following is not possible?

Ap=1p=1, q=2q=2, r=4r=4, s=3s=3
Bp=1p=1, q=3q=3, r=2r=2, s=4s=4
Cp=1p=1, q=4q=4, r=3r=3, s=2s=2
Dp=2p=2, q=4q=4, r=3r=3, s=1s=1
Ep=4p=4, q=3q=3, r=2r=2, s=1s=1

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