equation problem

Zidane

2011-05-24 11:18 pm

Theorem: If p, q, r are three distinct roots of ax^2 + bx + c = 0, then a=b=c=o.
Proof, the quadratic equation has at most two dintinct roots. If p, q, r are three distinct roots, then it is identically equal to 0. i.e. a = b =c =0

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回答 (1)

螞蟻雄兵

2011-05-24 11:37 pm

✔ 最佳答案

Theorem: If p，q，r are threedistinct roots of ax^2 + bx + c = 0，then a=b=c=o.
Proof，the quadraticequation has at most two dintinct roots. If p，q，r are three
distinct roots，then it isidentically equal to 0. i.e. a = b =c =0
Sol
p, q are two distinct roots of ax^2 + bx + c = 0
ap+aq=－b
p,r are two distinct roots of ax^2 + bx + c = 0
ap+ar=－b
ap+aq=ap+ar
aq=ar
aq－ar= 0
a(q－r)=0
q<>r
a=0
So
p，q are twodistinct roots of 0x^2 + bx + c = 0
bp+c=0，bq+c=0
bp=bq
b(p－q)=0
b=0
0x^2 + 0x + c = 0
c=0
So
a=b=c=0

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