Question

If u and v are the zeroes of the polynomial f(x)= x² + x + 1, then 1/u + 1/v =

Answer 1

f (x) = x^2 + x + 1

Where, a = 1 , b = 1 , c =1

One zero = u

Second zero = v

Sum of zeroes ( u + v ) = - b/a= -1 / 1 = -1

Product of zeroes ( u× v) = c/a = 1 / 1 = 1

We have to find value of , 1 / u+ 1 / v

Taking LCM

= u + v / uv

Keeping the values now,

= -1 / 1

= -1

Thus, 1 / u+ 1 / v = -1