If α and β are the zeroes of a polynomial x²-x-4 determine the value of α + β - αβ
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If α and β are the zeroes of a polynomial x²-x-4 determine the value of α + β - αβ
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Answer:
hope you understood it. don't comment on my writing it's good.
Step-by-step explanation:
Given, α,β are zeroes of the polynomial p(x)=x
2
−x−4, Then from the relation between the relation roots and co-efficients we get,
α+β=1.....(1) and α.β=−4......(2).
Now,
β
α
+
α
β
+3(
α
1
+
β
1
)−2αβ
=
α.β
α
2
+β
2
+3
α.β
α+β
−2α.β
=
α.β
(α+β)
2
−2α.β
+3
α.β
α+β
−2α.β
=−
4
9
−
4
3
+8 [ Using (1) and (2)]
=−3+8
=5.