SOLUTION: In one root ax^2+bX+c=0 is double the other.,prove that 2b^2=9ac ??????
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Question 818245
:
In one root ax^2+bX+c=0 is double the other.,prove that 2b^2=9ac ??????
Answer by
KMST(5328)
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The solutions to
are
,
which I will temporarily abbreviate as
with
.
If
,
which squares into
.
If
,
which squares into
.
Either way
which means
.
So
, and adding
to both sides we get
, which dividing both sides by 4 gives us
or
.