Question

If α, β are zeroes of quadratic polynomial 5x² + 5x + 1, find the value of 

1. α² + β²  

2. α⁻¹ + β^-1

Answer 1

P(x) = 5x² + 5x + 1

Answer 2

Quadratic Polynomial = 5x²+5x+1

α + β = -5/5= -1

αβ = 1/5

1.  α² + β²

α² + β² +2αβ- 2αβ
(α + β)²- 2αβ

(-1)²- 2/5 = 3/5

Answer =3/5

2.  1/α + 1/ β =

α + β/αβ = -1/1/5 =-5

Answer is = -5