C1 Exercise 3E Question 3a

Find the set of values of for which and
To solve this type of problem: (i) factorise the quadratic and use this to sketch it. Here becomes , hence roots at and . (ii) think about the values of which satisfy the quadratic inequality by considering whether you want the quadratic function to be < 0 or > 0. (iii) solve the linear inequality (iv) either simply by comparing your answers to (iii) and (iv) or by drawing them both on a number line and seeing where they're both true... (v) find the range of values for that satisfy both inequalities.