It is given that
$$f ( x ) = x ^ { 3 } - x ^ { 2 } + x - 6$$
Use the factor theorem to show that \(( x - 2 )\) is a factor of \(\mathrm { f } ( x )\).
6
Find the quadratic factor of \(\mathrm { f } ( x )\).
6
Hence, show that there is only one real solution to \(\mathrm { f } ( x ) = 0\)
6
Find the exact value of \(x\) that solves
$$\mathrm { e } ^ { 3 x } - \mathrm { e } ^ { 2 x } + \mathrm { e } ^ { x } - 6 = 0$$
\(7 \quad\) Curve \(C\) has equation \(y = x ^ { 2 }\)
\(C\) is translated by vector \(\left[ \begin{array} { l } 3 0 \end{array} \right]\) to give curve \(C _ { 1 }\)
Line \(L\) has equation \(y = x\)
\(L\) is stretched by scale factor 2 parallel to the \(x\)-axis to give line \(L _ { 1 }\)
Find the exact distance between the two intersection points of \(C _ { 1 }\) and \(L _ { 1 }\)