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let alpha be the common factor.
hence alpha = -a;
from polynomial x²+px+q=0 we find,
if alpha = -a then,
a²-ap+q=0; ------(i)
from polynomial x²+mx+n=0 we find,
if alpha = -a then
a²-ma+n=0; -------(ii)
Now, (i) - (ii) =>
-ap+am+q-n=0
=>a(m-p)-(n-q)=0
=>a=(n-q)/(m-p) [proved]
[PS: Help me level up by marking my answer as the brainliest. :) ]
hence alpha = -a;
from polynomial x²+px+q=0 we find,
if alpha = -a then,
a²-ap+q=0; ------(i)
from polynomial x²+mx+n=0 we find,
if alpha = -a then
a²-ma+n=0; -------(ii)
Now, (i) - (ii) =>
-ap+am+q-n=0
=>a(m-p)-(n-q)=0
=>a=(n-q)/(m-p) [proved]
[PS: Help me level up by marking my answer as the brainliest. :) ]
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