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.
a maths(Quadratic Equations)
2008-09-04 6:21 am
回答 (3)
2008-09-04 6:58 am
✔ 最佳答案
x2 log a+(x+1)log b=0i.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
2008-09-04 6:42 am
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
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
2008-09-04 6:32 am
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
==> 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
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