Question

Let g be a primitive fifth root of unity. Define a be any matrix. For a vevtor v= (v1, v2, v3, v4, v5)belong to r^5, define |v|a=√(|vav|) where v^t is transpose of v. If w=(1,-1,1,1,-1), then |w|a equals

Answer 1

p(x) =4x² - 4x - 3

=> 4x² - 6x + 2x - 3

=> 2x( 2x -3) + 1(2x + 3)

=> (2x + 1) (2x -3)

p(x) = 0

(2x + 1) = 0 or (2x-3) = 0

x=-1/2 or x= 3/2

Hence, -1/2 and 3/2 are the zeroes of p(x).