O Level Additional Maths Notes: Solving Quadratic Inequalities
We may be given the curve
and
asked to find the set of values of
for
which![]()
We can start by sketching the curve and obtain:

We can just read the solutions off here:
or
We
could have factorised the
expression for
to
obtain
and
solved
to
obtain
hence
the set of values of![]()
For the quadratic above, since the coefficient of
is
1 which is positive, we know it will be a “bum” curve,so the set
of solutions for
will
come in two parts,
or
![]()
The curve shown above is
We
are asked for example to find the set of values of
for
which
We
can see from the graph that there is only one set of values:
We
could have factorised the expression for
to
obtain
and
solved
to
obtain
hence
we could write down the set of values of![]()

The curve shown is![]()
We
are asked
to solve
The
curve is a “breast” curve and we can read off the solutions
or![]()
We can also factorise the expression for
to
obtain
and
solve
hence
finding the set of solutions just given.