Question

If α,β are the zeroes of the polynomial f(x) = x 2 +x+1 then find the value of α2+β2, α2-β2​

Answer 1

Answer:

f(x) = x²+x+1

let f(x)=0 => x²+x+1 = 0

x= -1+i(3)½ /2 , -1-i(3)½ /2

alpha = -1+i(3)½

beta = -1-i(3)½

=> (alpha)²+(beta)²=[-1+i(3)½]²+[-1-i(3)½]²

=1-3-2i(3)½+1-3+2i(3)½

=2-6

= -4

=>(alpha)²-(beta)²= -4i(3)½