Let N - be a 6 digit number all digits repeated and N is divisible by 924 and let - - be the roots of the equation x 2-11 x -0- If the products of all possible values of - is 168 k- then value of k is

N=αααααα=α (111111) is divisible by 3× 7× 11 Hence for N to be divisible by 924, α=4 or 8 nbsp; and α and β are roots of the equation x^2 11x+λ=0 α+β=11 (α ...

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Standard XII

Mathematics

Sequence

Let N =αααααα...

Question

Let $N = α α α α α α$ be a $6$ digit number (all digits repeated) and $N$ is divisible by $924$ and let $α, β$ be the roots of the equation $x^{2} - 11 x + λ = 0$ . If the products of all possible values of $λ$ is $168 k$ , then value of $k$ is

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Solution

$N = α α α α α α = α (111111)$ is divisible by $3 \times 7 \times 11$

Hence for $N$ to be divisible by $924, α = 4 or 8$
and $α$ and $β$ are roots of the equation $x^{2} - 11 x + λ = 0 α + β = 11 (α, β) = (4, 7) or (8, 3)$

possible value of $λ = 28, 24$
The product of $λ = 672$

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Let N=αααααα be a 6 digit number (all digits repeated) and N is divisible by 924 and let α,β be the roots of the equation x2−11x+λ=0. If the products of all possible values of λ is 168k, then value of k is

N=αααααα=α(111111) is divisible by 3×7×11 Hence for N to be divisible by 924,α=4 or 8 and α and β are roots of the equation x2−11x+λ=0α+β=11(α,β)=(4,7) or (8,3) possible value of λ=28,24 The product of λ=672

Let $N = α α α α α α$ be a $6$ digit number (all digits repeated) and $N$ is divisible by $924$ and let $α, β$ be the roots of the equation $x^{2} - 11 x + λ = 0$ . If the products of all possible values of $λ$ is $168 k$ , then value of $k$ is

$N = α α α α α α = α (111111)$ is divisible by $3 \times 7 \times 11$

Hence for $N$ to be divisible by $924, α = 4 or 8$
and $α$ and $β$ are roots of the equation $x^{2} - 11 x + λ = 0 α + β = 11 (α, β) = (4, 7) or (8, 3)$

possible value of $λ = 28, 24$
The product of $λ = 672$