Lf - - are the roots of the equation x2-mx-l-0 and - - that of x2-nx-l-0- then the value of -

The correct option is C l(m n)^2 (α γ )(β γ )=αβ (α +β)γ +γ ^2 nbsp; nbsp;...(1) (α δ )(β δ )=αβ (α +β)δ +δ ^2 nbsp; nbsp;...(2) ...

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Standard XII

Mathematics

Sum of Infinite Terms

lf α, β are...

Question

lf $α, β$ are the roots of the equation $x^{2} + m x + l = 0$ and $γ, δ$ that of $x^{2} + n x + l = 0$ , then the value of $(α - γ) (β - γ) (α - δ) (β - δ) =$

l (m + n)^{2}

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- l (m + n)^{2}

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l (m - n)^{2}

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1 (m + n)

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Solution

The correct option is C $l (m - n)^{2}$
$(α - γ) (β - γ) = α β - (α + β) γ + γ^{2}$ ...(1)
$(α - δ) (β - δ) = α β - (α + β) δ + δ^{2}$ ...(2)
$α + β = - m; α β = l; γ + δ = - n; γ δ = l$
$∴ α β = γ δ = l$
$l + γ^{2} = - n γ$ and $l + δ^{2} = - n δ$ ...(3)
Substituting the roots in the second equation
From (1), (2), and (3), we get
$(α - γ) (β - γ) (α - δ) (β - δ) = (l + m γ + γ^{2}) (l + m δ + δ^{2})$
$= (m - n)^{2} γ δ$
$= (m - n)^{2} l$

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Similar questions

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Q. If

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lf α, β are the roots of the equation x2+mx+l=0 and γ, δ that of x2+nx+l=0, then the value of (α−γ)(β−γ)(α−δ)(β−δ)=

lf $α, β$ are the roots of the equation $x^{2} + m x + l = 0$ and $γ, δ$ that of $x^{2} + n x + l = 0$ , then the value of $(α - γ) (β - γ) (α - δ) (β - δ) =$