Question 1019a

${C}$ crosses the ${x\textrm{-axis}}$ at the point with coordinates ${(a,0).}$ Find the value of ${a}$ correct to ${3}$ decimal places.

You are given that ${b>a.}$

The region ${P}$ is bounded by ${C,}$ the ${x\textrm{-axis}}$ and the lines ${x=-1}$ and ${x=0.}$ The region ${Q}$ is bounded by ${C,}$ the line ${x=b}$ and part of the the ${x\textrm{-axis}}$ between ${x=a}$ and ${x=b.}$

Given that the area of ${Q}$ is ${8}$ times the area of ${P,}$ find the value of ${b}$ correct to ${3}$ decimal places.