Question

If α, β are the zeroes of the polynomial x² - 3x + 5 ,then α/β + β/α​

Answer 1

Answer:

Step-by-step explanation:

x² - 3x + 5

It is in the form of ax² - bx + c

α and β are the zeros of the polynomial

α + β = -b/a = -(-3)/1 = 3

αβ = c/a = 5/1 = 5

(α)^2 + (β)^2 = (α + β)^2 - 2(αβ) = (3)^2 - 2(5)

(α)^2 + (β)^2 = 9 - 10 = -1

α/β + β/α = ((α)^2 + (β)^2) / αβ

α/β + β/α = -1/5

Used Formula

A^2 + B^2 = (A+B)^2 - 2AB