Question

If α and 1/α are the zeroes of the polynomial 4x^2-2x+1(p-1).Find the value of p.

Answer 1

P(x) =  4 x²  - 2 x + (p-1)  = a x²  + b x + c

sum of roots:  α + 1/α  =  -b/a = 2/4 = 1/2

product of roots :    α * 1/α  =  c/a  = (p - 1) / 4
        =>  p - 1 =  4
        =>   p = 5