Question

if alpha and beta are the zeroes of the polynomial 6x2+x-2 find the value og alpha/beta + beta/alpha

Answer 1

Heya buddy,


Here is your answer,



Hope it helps you,
Thank you.

Answer 2

The value of α/β+β/α is -25/12.

Given,

A quadratic equation with α and β as its zeroes.

To Find,

The value of α/β+β/α.

Solution,

The given equation is

6x²+x-2 = 0

Now,

Sum of zeroes = α+β = -b/a

α+β = -1/6

Product of zeroes = αβ = c/a

αβ = -2/6 = -1/3

Now,

α/β+β/α = (α²+β³)/αβ

First, we will find the value of

α²+β³ = (α+β)²-2αβ = (-1/6)²-2(-1/3) = 1/36+2/3 = (1+24)/36 = 25/36

Now,

α/β+β/α = (25/36)/(-1/3) = - 25/12

Hence, the value of α/β+β/α is -25/12.