3 The diagram in the Printed Answer Booklet shows part of the graph of \(y = x ^ { 2 } - 4 x + 3\).
- It is required to solve the equation \(x ^ { 2 } - 3 x + 1 = 0\) graphically by drawing a straight line with equation \(y = m x + c\) on the diagram, where \(m\) and \(c\) are constants.
Find the values of \(m\) and \(c\).
- Use the graph to find approximate values of the roots of the equation \(x ^ { 2 } - 3 x + 1 = 0\).
- By shading, or otherwise, indicate clearly the regions where all of the following inequalities are satisfied. You should use the values of \(m\) and \(c\) found in part (a).
\(x \geqslant 0\)
\(x \leqslant 4\)
\(y \leqslant x ^ { 2 } - 4 x + 3\)
\(y \geqslant m x + c\)