Solving Quadratic Inequalities

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We may be given the curveand asked to find the set of values offor 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 forto obtainand solvedto obtainhence the set of values of

For the quadratic above, since the coefficient ofis 1 which is positive, we know it will be a “bum” curve,so the set of solutions forwill come in two parts,or

The curve shown above isWe are asked for example to find the set of values offor whichWe can see from the graph that there is only one set of values:We could have factorised the expression forto obtainand solvedto obtainhence we could write down the set of values of

The curve shown isWe are asked

to solveThe curve is a “breast” curve and we can read off the solutionsor

We can also factorise the expression forto obtain and solvehence finding the set of solutions just given.

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