OCR FP1 AS 2018 March — Question 2

Exam BoardOCR
ModuleFP1 AS (Further Pure 1 AS)
Year2018
SessionMarch
TopicRoots of polynomials

2 In this question you must show detailed reasoning.
The quadratic equation \(3 x ^ { 2 } - 7 x + 5 = 0\) has roots \(\alpha\) and \(\beta\).
  1. Write down the values of \(\alpha + \beta\) and \(\alpha \beta\).
  2. Hence find the values of the following expressions.
    (a) \(\frac { 1 } { \alpha } + \frac { 1 } { \beta }\)
    (b) \(\alpha ^ { 2 } + \beta ^ { 2 }\)
    \(3 \quad l _ { 1 }\) and \(l _ { 2 }\) are two intersecting straight lines with the following equations. $$\begin{aligned} & l _ { 1 } : \mathbf { r } = \left( \begin{array} { c }