TMUA 2018 Paper 2 Q15 — Worked Solution

P2·Algebra & Surds, Functions, Transformations & Graphs +1·7.5Official · 2018 · Q15

cubicthree-real-rootsvertical-shifthorizontal-shiftreflection

It is given that

f (x) = x^{3} + 3 q x^{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?

The equation

f (x) + 1 = 0

has

3

distinct real roots.

The equation

f (x + 1) = 0

has

3

distinct real roots.

III

The equation

f (- x) - 1 = 0

has

3

distinct real roots.

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