The product of two roots of x^3– 2x^2 + kx + 21 = 0 is 7. Calculate k.
8
0-8
O1
None of these
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3
Answer:
Let α,β,γ,δ be the roots of x
4
−x
3
+2x
2
+kx+17=0
Such that α+β=γ+δ
Then s
1
=α+β+γ+δ=1⇒α+β=
2
1
s
2
=αβ+αγ+αδ+βγ+βδ+γδ=2⇒(α+β)
2
+αβ+γδ=2
⇒αβ+γδ=2−
4
1
=
4
7
...(1)
s
3
=αβγ+αβδ+αγδ+βγδ=−k⇒(α+β)(αβ+γδ)=−k
⇒(αβ+γδ)=−2k ...(2)
From (1) and (2), we have
−2k=
4
7
⇒k=−
8
7
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