the degree of the polynomial;

the value of ${a_0}$.

the sum of the roots of the polynomial $= \frac{{63}}{{16}}$     (A1)

$2\left( {\frac{{1 - {{\left( {\frac{1}{2}} \right)}^n}}}{{1 - \frac{1}{2}}}} \right) = \frac{{63}}{{16}}$     M1A1

Note:     The formula for the sum of a geometric sequence must be equated to a value for the M1 to be awarded.

$1 - {\left( {\frac{1}{2}} \right)^n} = \frac{{63}}{{64}} \Rightarrow {\left( {\frac{1}{2}} \right)^n} = \frac{1}{{64}}$

$n = 6$     A1

[4 marks]

$\frac{{{a_0}}}{{{a_n}}} = 2 \times 1 \times \frac{1}{2} \times \frac{1}{4} \times \frac{1}{8} \times \frac{1}{{16}},{\text{ (}}{{\text{a}}_n} = 16)$     M1

${a_0} = 16 \times 2 \times 1 \times \frac{1}{2} \times \frac{1}{4} \times \frac{1}{8} \times \frac{1}{{16}}$

${a_0} = {2^{ - 5}}\;\;\;\left( { = \frac{1}{{32}}} \right)$     A1

[2 marks]

Total [6 marks]