TMUA 2022 Paper 1 Q18 — Worked Solution

P1·Functions, Transformations & Graphs, Inequalities·8.0Official · 2022 · Q18

polynomial-rootsgraph-intersectiondouble-roots

It is given that

f (x) = x^{2} (x - 1)^{2} (x - 2)

g (x) = - p (x - q)^{2} (x - r)^{2}

where

p

q

and

r

are positive and

q < r

.Find the set of values of

q

and

r

that guarantees the greatest number of distinct real solutions of the equation

f (x) = g (x)

for all

p

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