Problem 5.5.9's answer in the back of the book sure looks like
it's wrong. When I crank it out by hand I get the answers
alpha = sqrt(5/7), a=c=7/25, b=8/75.
This is based on the assumption that the only place that the x^2 gets
into the act is when you are calculating the values for the solution
vector, in other words that you're solving the system
/ \ / \ | 1 1 1 | a |2/3| | -@ 0 @ | b = | 0 | | @^2 0 @^2 | c |2/5| (where @ = alpha) | -@^3 0 @^3 | | 0 | | @^4 0 @^4 | |2/7| \ / \ /
if this is the case, then I'm pretty darn sure of my answer because it
verifies out for everything from f(x)=1 through x^5.
--JMike