TMUA Official 2018 Paper 2 · Question 15 · ExamDay

Official papers

Official 2018 Paper 2 · Q15

Paper 2Logic & proofAlgebra

It is given that $f(x)=x^3+3qx^2+2$ , where $q$ is a real constant.

The equation $f(x)=0$ has 3 distinct real roots.

Which of the following statements is/are necessarily true?

I The equation $f(x)+1=0$ has 3 distinct real roots.
II The equation $f(x+1)=0$ has 3 distinct real roots.
III The equation $f(-x)-1=0$ has 3 distinct real roots.

Anone of them

BI only

CII only

DIII only

EI and II only

FI and III only

GII and III only

HI, II and III

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