Question

$\alpha + \beta$ are the roots $x^{2} -2x+1$=0 then

1.$\alpha> \beta$
2.$\alpha < \beta$
3.$\alpha + \beta =0$
4.$\alpha = \beta$
 which of the following are correct?

Answer 1

we use discriminant for this purpose
for eq. ax² + bx + c = 0
D = b² - 4ac

So conditions are D > 0 then roots are real and distinct
                           D = 0 then roots are real and equal
                           D < 0 then roots are imaginary and distinct

so here for the eq.  x² - 2x + 1 = 0

is D = (-2)² - 4 x 1 x 1 = 4 - 4 = 0 

So roots are real and equal

so 4) α = β