These Ten-Year-Series (TYS) worked solutions with video explanations for 2005 A Level H2 Mathematics are suggested by Mr Gan. For any comments or suggestions please contact us at support@timganmath.edu.sg.
Verify that $z=\text{i}$ is a root of the equation
${{z}^{4}}-2{{z}^{3}}+6{{z}^{2}}-2z+5=0$.
[1]
Hence determine the other roots.
[4]
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It is given that $a$, $b$, $c$ are the first three terms of a geometric progression. It is also given that $a$, $c$, $b$ are the first three terms of an arithmetic progression.
(i)
Show that ${{b}^{2}}=ac$ and $c=\frac{a+b}{2}$.
[2]
(i) Show that ${{b}^{2}}=ac$ and $c=\frac{a+b}{2}$.
[2]
(ii)
Hence show that $2{{\left( \frac{b}{a} \right)}^{2}}-\left( \frac{b}{a} \right)-1=0$.
[2]
(ii) Hence show that $2{{\left( \frac{b}{a} \right)}^{2}}-\left( \frac{b}{a} \right)-1=0$.
[2]
(iii)
Given that the sum to infinity of the geometric progression is $S$, find $S$ in terms of $a$.
[4]
(iii) Given that the sum to infinity of the geometric progression is $S$, find $S$ in terms of $a$.
[4]
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