The inequality is .
As the symbol is and
, the solution lies between the solutions of the equation.
The related function is .
Solve the inequality.
\ (Related function)
(Quadratic formula)
(Substitute
and
)
(Simplify)
or
(Write as two equation)
or
(Simplify)
Graph:
\Graph the parabola and the -intercepts at
and
.
Observe the graph:
\The graph lies below the -axis between
and
.
The solution set of the inequality is .
Check:
\Test one value of -greater than
and less than
of the original inequality.
Case(i):
(Original function)
(Substitute
)
(Evaluate powers:
)
(Multiply)
(Simplify)
Case(ii):
(Original function)
(Substitute
)
(Evaluate powers:
)
(Multiply)
(Simplify)
Case(iii):
(Original function)
(Substitute
)
(Evaluate powers:
)
(Multiply)
(Simplify)
Solution set is .