kill(all)$

fpprintprec:6;

van=facebook.com/LearningCalculus$

P(x):=a*x^5+b*x^4+c*x^3+d*x^2+e*x+f;

PPrime(x):=''(diff(P(x),x))$ PPrime(x);

PPPrime(x):=''(diff(P(x),x,2))$PPPrime(x);

first(expand(PPrime(P(x))))=
first(expand(P(PPrime(x))));

solve(%,a);

second(expand(PPrime(P(x))))=
second(expand(P(PPrime(x))));

2*b=2*b;

solve(%,b);

first(PPPrime(first(fullratsimp(PPrime(P(x))))))=
first(P(first(fullratsimp(PPrime(PPPrime(x))))));

s:solve(%,a)$

for i: 1 thru 10 do
    print("Answer ",s[i], "  float: ", float(rectform(s[i])), " inverse ", 1/float(rectform(s[i])));

print("Answer ", s[11])$

S:unique(s);

for i: 2 thru 10 do
    print("Answer ",S[i], "  imag/real: ", float(imagpart(rectform(rhs((S[i]))))/realpart(rectform(rhs((S[i]))))));