Question

if alpha and beta are zeros of p(x)= x²+x+1, then find the value of 1\alpha+1\Beta and alpha ²+beta ²

Answer 1

1/alpha+1/beta=-1. alpha square + beta square =-1

Answer 2

• x² + x + 1 = 0
• here : a = 1 , b = 1 , c = 1
• Sum of Zeros = α+β = -b/a = -1/1 = -1
• Product of Zeros = αβ = c/a = 1/1 = 1
• 1/α + 1/β = α+β/αβ = -1/1 = -1
• α² + β² = α² + β² + 2αβ = -1 + 2 = 1