12
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\includegraphics[alt={},max width=\textwidth]{fecb40da-cf47-45e0-801a-1d3d8811b5a0-3_840_919_849_612}
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\caption{Fig. 12}
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Fig. 12 shows the graph of \(y = \frac { 4 } { x ^ { 2 } }\).
- On the copy of Fig. 12, draw accurately the line \(y = 2 x + 5\) and hence find graphically the three roots of the equation \(\frac { 4 } { x ^ { 2 } } = 2 x + 5\).
- Show that the equation you have solved in part (i) may be written as \(2 x ^ { 3 } + 5 x ^ { 2 } - 4 = 0\). Verify that \(x = - 2\) is a root of this equation and hence find, in exact form, the other two roots.
- By drawing a suitable line on the copy of Fig. 12, find the number of real roots of the equation \(x ^ { 3 } + 2 x ^ { 2 } - 4 = 0\).