Question 985658

Please solve:
Given that the root of ax^2+bx+2=0 is 2-{{{sqrt(2)}}}, find the values of a and b, and the other root. (assume a and b are integers)  

Thanks.
<pre>Since one root is: {{{2 - sqrt(2)}}}, then other root is: {{{highlight_green(2 + sqrt(2))}}}
Sum of roots: {{{2 - sqrt(2) + 2 + sqrt(2)}}} = 4
Sum of roots: {{{- b/a}}}, so {{{- b/a = 4}}} --------- eq (i)

Product of roots: {{{(2 - sqrt(2))(2 + sqrt(2))}}} -----> 4 - 2, or 2
Product of roots: {{{c/a}}}, so {{{c/a = 2}}}_____{{{2/a = 2}}}_____{{{2a = 2}}}______{{{highlight_green(a = 1)}}} 
{{{- b/1 = 4}}} ---------- Substituting 1 for a in eq (i)
- b = 4 ---------- Cross-multiplying
{{{highlight_green(b = - 4)}}}