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Question

If two roots of the equation 4x22x3=0 are a and b, then find out the value of a2b+b2a.


Solution


4x22x3=0
Let a and b be the roots (we cannot type alpha and beta here, hence we call it a and b)
a+b=24=12
ab=34
a2b+b2a=(a3+b3)ab    ...(I)
Now you know the identiry a3+b3=(a+b)33ab(a+b)
Substituting on RHS:
a3+b3=(1)33(34)(12)
=18+98=108
Substituting in (i),
a2b+b2a=(108)(34)
=4024=53=1.6667

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