1 The quadratic equation \(x ^ { 2 } - 6 x + 14 = 0\) has roots \(\alpha\) and \(\beta\).
- Write down the value of \(\alpha + \beta\) and the value of \(\alpha \beta\).
- Find a quadratic equation, with integer coefficients, which has roots \(\frac { \alpha } { \beta }\) and \(\frac { \beta } { \alpha }\).
[0pt]
[5 marks]
\(2 \quad\) A curve \(C\) has equation \(y = ( 2 - x ) ( 1 + x ) + 3\). - A line passes through the point \(( 2,3 )\) and the point on \(C\) with \(x\)-coordinate \(2 + h\). Find the gradient of the line, giving your answer in its simplest form.
- Show how your answer to part (a) can be used to find the gradient of the curve \(C\) at the point \(( 2,3 )\). State the value of this gradient.
[0pt]
[2 marks]