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The diagram shows the curve \(y = \sqrt { x } - 3\). The shaded region is bounded by the curve and the two axes.
Find the exact area of the shaded region.
\(2 \mathrm { f } ( x )\) is a cubic polynomial in which the coefficient of \(x ^ { 3 }\) is 1 . The equation \(\mathrm { f } ( x ) = 0\) has exactly two roots.
- Sketch a possible graph of \(y = \mathrm { f } ( x )\).
It is now given that the two roots are \(x = 2\) and \(x = 3\).
- Find, in expanded form, the two possible polynomials \(\mathrm { f } ( x )\).