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Official 2023 Paper 1 · Q14

Paper 1Functions & graphsAlgebra

The function

f(x)=23x3+2mx2+n,m>0f(x)=\frac23x^3+2mx^2+n,\qquad m>0

has three distinct real roots.

What is the complete range of possible values of nn, in terms of mm?

A−83m3<n<0-\frac83m^3<n<0
B−43m3<n<0-\frac43m^3<n<0
C0<n<32m20<n<\frac32m^2
D0<n<403m30<n<\frac{40}3m^3
En<−83m3n<-\frac83m^3
Fn<32m2n<\frac32m^2
Gn>−43m3n>-\frac43m^3
Hn>403m3n>\frac{40}3m^3

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