TMUA Official 2022 Paper 1 · Question 18

Official papers

Official 2022 Paper 1 · Q18

Paper 1Algebra

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 $p$ .

q<1

and

r<1

q<1

and

1<r<2

q<1

and

r>2

1<q<2

and

1<r<2

1<q<2

and

r>2

q>2

and

r>2

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