Question

if α, β are zeros of 3x² - 4x +1, find value of a) α/β+ β/α b) α²/β + β²/α​

Answer 1

hey buddy

hope it will be helpful to you

Answer 2

Hey there!

Given,

α , β are zeroes of 3x² - 4x + 1.

Factorize  the polynomial:

3x² - 4x + 1

= 3x² -3x - x + 1  

= 3x( x - 1)  - 1(x - 1)

= (x - 1) (3x - 1)

So, x-1= 0   or   3x - 1 = 0

x = 1     or,  x = 1/3

Then,  α = 1 and β = 1 /3

a) α / β  +  β / α

= 1 / (1÷3) + (1÷3) / 1

= 3 / 1   +  1 / 3

= 10 / 3

b) α² / β   + β²/α

= 1² / (1÷3)   + (1÷3)² / 1

= 3/1  + 1/9

= 28 / 9

Hope it Helps You!