Question

if alpha and beta are the roots of polynomial x ^2 - 3 x + 4 then find 1/alpha and 1/ beeta​

Answer 1

Answer:

sum of roots = -b/a    = α +β

product of roots = c/a = αβ

Step-by-step explanation:

x ^2 - 3 x + 4

∴a = 1     b =  -3    c = 4

β = c/aα

∴α +β = -b/a

α +c/aα  = -b/a

=aα^2 +bα +c

=α^2  -3α + 4

α = +3±√7i/2

α + β = -b/a

α + β =3

β  = 3 + [3 ±√7i]/2

= [9±√7i]/2

∴1/α = 2/[3±√7i]

∴1/β = 2/[9±√7i]