Question

# If two roots of the equation 4x2−2x−3=0 are a and b, then find out the value of a2b+b2a.

Solution

## 4x2−2x−3=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)3−3ab(a+b) Substituting on RHS: a3+b3=(1)3−3(−34)(12) =18+98=108 Substituting in (i), a2b+b2a=(108)(−34) =−4024=−53=−1.6667

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