00:01
In this question, we need to solve the equation x to the power 11 minus 1 is equal to 0.
00:09
And we need to reduce the value of sine pi by 11, sine 2 pi by 11, sine 3 pi by 11, sine 3 pi by 11, 1, sine 5 pi by 11.
00:37
Let's see how to solve this question.
00:41
The given equation is f to the power minus 1 is equal to 0.
00:49
The roots of the above equation can be given as cost 2k pi by 11 plus minus iota sine 2k pi by 11 where k is 1.
01:16
Is equal to 0, 1, 2, 3, 4, 5.
01:28
When the value of k is equal to 0, then it gives x is equal to 1.
01:40
Hence, the roots of the equation, equation x to the power 10 plus x to the power 9 plus x to the power 8 plus so on, plus x to the power 2 plus x plus 1 is equal to 0 will be cos 2 k pi by 11 plus minus iota sign 2 k pi by 11 where k is equals to 1 2 3 4 5 let's say this is equation 1 and based on the calculations the roots of the equation 1 can also be written as x minus cos 2k pi by 11 minus iota sign 2k pi by 11 into x minus plus cos 2k pi by 11 plus iota sign 2k pi by 11.
03:30
Here k is equals to 1, 2, 3, 4, 5 are the factors of left -hand side of the equation 1...