If 1- -1- -2- -3- -4- -5- -6- are seven- 7th root of unity them -3-13-33-5- is-

The correct option is B √(1093) x^7 1 = 0 (x 1)(x α_1).....(x α_6) = x^7 1 Putting x=3 , we get 2.(x α_1).(x α_2)...(x α_6) = 2186 ...

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Standard XII

Mathematics

Binomial Expression

If 1, α1, α...

Question

If $1, α_{1}, α_{2}, α_{3}, α_{4}, α_{5}, α_{6}$ , are seven, $7^{t h}$ root of unity them $| (3 - α_{1}) (3 - α_{3}) (3 - α_{5}) |$ is?

\sqrt{2186}

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\sqrt{1093}

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\sqrt{1023}

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\sqrt{511}

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Solution

The correct option is B $\sqrt{1093}$
$x^{7} - 1 = 0$
$(x - 1) (x - α_{1}) . . . . . (x - α_{6}) = x^{7} - 1$
Putting $x = 3$ , we get
$2. (x - α_{1}) . (x - α_{2}) . . . (x - α_{6}) = 2186$
$| (x - α_{1}) |^{2} | (x - α_{3}) |^{2} | (x - α) |^{2} = 1093$
$| (x - α_{1}) (x - α_{3}) (x - α_{5}) | = \sqrt{1093}$

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Similar questions

Q. If

α_{1} < α_{2} < α_{3} < α_{4} < α_{5} < α_{6}

, then the equation

(x - α_{1}) (x - α_{2}) (x - α_{3}) (x - α_{5}) + 3 (x - α_{2}) (x - α_{4}) (x - α_{6}) = 0

has

1, $α$ , $α^{2}$ ,............................ $α^{6}$ are the roots of the equation x = $(1)^{\frac{1}{7}}$ .Find the quadratic equation whose roots are A = $α$ + $α^{2}$ + $α^{4}$ , B = $α^{3}$ + $α^{5}$ + $α^{6}$ .

Q. Let

α = c i s \frac{2 π}{7}, β = α + α^{2} + α^{4}

and

γ = α^{3} + α^{5} + α^{6}

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β

and

γ

are the roots of the equation

Q. If

α = cos \frac{2 π}{7} + i sin \frac{2 π}{7}

and

p = α + α^{2} + α^{4}

and

q = α^{3} + α^{5} + α^{6},

then find the equation whose roots are

p

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If 1, $α$ , $α^{2}$ , $α^{3}$ ,................. $α^{6}$ are the roots of the equation x = $(- 1)^{\frac{1}{7}}$ .Find the value of

$α^{4}$ + $α^{6}$ + $α^{7}$ + $α^{5}$ + $α^{7}$ + $α^{8}$ + $α^{7}$ + $α^{9}$ + $α^{10}$

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If 1,α1,α2,α3,α4,α5,α6, are seven, 7th root of unity them |(3−α1)(3−α3)(3−α5)| is?

The correct option is B √1093x7−1=0(x−1)(x−α1).....(x−α6)=x7−1Putting x=3, we get2.(x−α1).(x−α2)...(x−α6)=2186|(x−α1)|2|(x−α3)|2|(x−α)|2=1093|(x−α1)(x−α3)(x−α5)|=√1093

If $1, α_{1}, α_{2}, α_{3}, α_{4}, α_{5}, α_{6}$ , are seven, $7^{t h}$ root of unity them $| (3 - α_{1}) (3 - α_{3}) (3 - α_{5}) |$ is?