1. If α,β are zeroes of the quadratic polynomial x2 -6x+10, find the value of α3+β3.
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Step-by-step explanation:
Consider the given polynomial.
f(x)=ax
2
+bx+c ……. (1)
Since, α and β are the zeroes of given polynomial.
So,
α+β=−
a
b
αβ=
a
c
Therefore,
α
3
+β
3
⇒(α+β)
3
−3αβ(α+β)
⇒(−
a
b
)
3
−
a
3c
(−
a
b
)
⇒−
a
3
b
3
+
a
2
3bc
⇒
a
3
−b
3
+3abc
Hence, this is the answer.
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