Grade 12th passAlgebra
if 1,a1,a2......an-1are n roots of unity , then the value of (1-a1)(1-a2).....(1-an-1) is?
if 1,a1,a2......an-1are n roots of unity , then the value of (1-a1)(1-a2).....(1-an-1) is?
3 Answers
Nishant Vora
Basically 1,a1,a2......an-1 all these are the roots of this equation x3 – 1 =0
So I can write
Put x=1 on both the sides now
Ans =3
So I can write
Put x=1 on both the sides now
Ans =3
Jayakeerti
x^n - 1/(x-1) = (x-@1)(x-@2)......(x-@n-1)
(x^(n-1) +x^(n-2)1 + ...... + 1^(n-1))
Put x = 1
Thus, answer is n
Kushagra Madhukar
Dear student,
Please find the solution to your problem below.
x3 – 1 = (x – 1)(x – a1)(x – a2)......(x – an-1)
Hence, (x3 – 1) / (x – 1) = (x – a1)(x – a2)......(x – an-1)
or, (x2 + x + 1) = (x – a1)(x – a2)......(x – an-1)
Put x = 1
Hence, (1 – a1)(1 – a2)........(1 – an-1) = (12 + 1 + 1) = 3
Hence the answer is 3
Hope it helps.
Thanks and regards,
Kushagra
Other Related Questions on algebra
How do you write “the product of 18 and q” as an algebraic expression?
How do you write “the product of 18 and q” as an algebraic expression?
algebra
Last Activity: 2 Years ago