0580 P42 - Nov 2019 - Q5 - 17 marks
13911
\(y=\frac{x^2}2+\frac1{x^2}-\frac2x,\quad x\ne0\).
| x | -3 | -2 | -1 | -0.5 | -0.3 | 0.2 | 0.3 | 0.5 | 1 | 2 | 3 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| y | 5.3 | 3.3 | … | 8.1 | 17.8 | … | 4.5 | 0.1 | -0.5 | 1.3 | … |
(a) Complete the table. [3]
(b) Draw the graph for \(-3\le x\le-.3\) and \(.2\le x\le3\). [5]
(c) Use the graph to solve \(\frac{x^2}2+\frac1{x^2}-\frac2x\le0\). [2]
(d) Find the smallest positive integer k for which \(\frac{x^2}2+\frac1{x^2}-\frac2x=k\) has two solutions within the stated intervals. [1]
(e(i)) Draw a suitable straight line to solve \(\frac{x^2}2+\frac1{x^2}-\frac2x=3x+1\) in the stated intervals. [3]
(e(ii)) Rewrite this equation as \(x^4+ax^3+bx^2+cx+2=0\). Find a, b, c. [3]
