a maths(Quadratic Equations)

x2 log a+(x+1)log b=0
i.e. x2loga + xlogb +logb=0

The quadratic equation has two non-zero equal roots,
∴△=0
(logb)2-4(loga)(logb)=0
logb(logb-4loga)=0
4loga=logb
a4=b
a=b1/4//




2008-09-03 22:59:14 補充：
a^4=b
b=a^4

the quadratic equation

x^2 log a+(x+1)log b=0,

where a,b are two positive constants , has two non-zero equal roots.

Express b in terms of a.

Δ=(log b)^2 -4(log a)(log b)=0
log b -4(log a)=0
log b -log a^4=0
log b =log a^4
b = a^4

the root is (-log b)/(2 log a) =/= 0
==> log b =/= 0
Δ=(log b)^2 - 4(log a)(log b)=0
Since log b =/= 0, log b can be divided on both sides.
log b - 4 log a = 0
log b = log a^4
b = a^4