TMUA Practice Question — Worked Solution

P2·Functions, Transformations & Graphs, Algebra & Surds +1·7.5CrackTMUA Original

modulus-equationroot-countingmust-be-truemulti-statementhidden-case-splitcounterexample

Let

f (x) = a x^{2} + b x + c

, where

a

b

and

c

are real constants with

a \neq = 0

. It is given that the equation

∣ f (x) ∣ = 1

has exactly three distinct real solutions. Nothing further is known about

a

b

and

c

The equation

f (x) = - 1

has exactly one real solution.

The equation

∣ f (x) ∣ = 2

has exactly two distinct real solutions.

III

The equation

f (x) = 0

has two distinct real solutions whose difference is at least

2

Which of the above must be true?

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