If α, β γ are the roots of the equation x 3+ px + q =0, then the value of the determinant |α β γ β γ α γ α β|=

Question

If α, β &gamma; are the roots of the equation x 3+ px + q =0, then the value of the determinant |α β &gamma; β &gamma; α &gamma; α β|= (A) p (B) q (C) p2-2 q (D) none

Tardigrade Admin · Accepted Answer

operatornamedet S C D=α3+β3+&gamma;3-3 α β &gamma; Suppose given α+β+&gamma;=0 as coefficient of x2=0 Now operatornamedet(α+β+&gamma;)|1 1 1 β &gamma; α &gamma; α β|=0 ⇒( D )

Q. If $α, β & γ$ are the roots of the equation $x^{3} + p x + q = 0$ , then the value of the determinant $∣ ∣ α β γ β γ α γ α β ∣ ∣ =$

$p$

$q$

$p^{2} - 2 q$

none

$det SC D = α^{3} + β^{3} + γ^{3} - 3 α β γ$
Suppose given $α + β + γ = 0$
as coefficient of $x^{2} = 0$
Now $det (α + β + γ) ∣ ∣ 1 β γ 1 γ α 1 α β ∣ ∣ = 0 \Rightarrow (D)$

Q. If α,β&γ are the roots of the equation x3+px+q=0, then the value of the determinant ∣∣​αβγ​βγα​γαβ​∣∣​=

p

q

p2−2q

none

detSCD=α3+β3+γ3−3αβγ Suppose given α+β+γ=0 as coefficient of x2=0 Now det(α+β+γ)∣∣​1βγ​1γα​1αβ​∣∣​=0⇒(D)

Q. If $α, β & γ$ are the roots of the equation $x^{3} + p x + q = 0$ , then the value of the determinant $∣ ∣ α β γ β γ α γ α β ∣ ∣ =$

$p$

$q$

$p^{2} - 2 q$

$det SC D = α^{3} + β^{3} + γ^{3} - 3 α β γ$
Suppose given $α + β + γ = 0$
as coefficient of $x^{2} = 0$
Now $det (α + β + γ) ∣ ∣ 1 β γ 1 γ α 1 α β ∣ ∣ = 0 \Rightarrow (D)$