AP EAMCET2002MathematicsComplex Number
If 1+ 3 i 2 is a root of the equation x^4-x^2+x-1=0 . Then, its real roots are
Options
- A1,1
- B-1,-1
- C1,2
- D1,-1
Correct answer
D. 1,-1
Step-by-step solution
We have, Let gathered x^4-x^2+x-1=0 = 1+ 3 i 2 , = 1- 3 i 2 + = 1+ 3 i 2 + 1- 3 i 2 =1 = ( 1+ 3 i 2 ) ( 1- 3 i 2 )= 1+3 4 =1 gathered Then equation is x^2-( + ) x+ =0 x^2-x+1=0 Now, divide x^4-x^2+x-1 by x^2-x+1 , We get, x^2-1 The real roots are x^2-1=0 x= 1