Question

If alpha and beta are the zeros and the polynomial x square minus x minus 4 then the value of one upon alpha + 1 upon the minus Alpha into beta is is

Answer 1

Solution :

Given polynomial :

p(x) = x^2 - x - 4

α and β are the zeroes of this polynomial .

We know that;

For any polynomial of the form ax^2 + bx + c ;

If α and β are the roots

α + β = ( -b/a)

αβ = (c/a)

Here ;

α + β = 1

αβ = -4

> α = -4/β

Placing this into the first equation ;

> β - 4/β = 1

> β^2 - 4 = β

> β^2 - β - 4 = 0

> β = [ 1 ± √17 ]/2

> β = 2.561 { We are discarding the negative value }

> α = -1.561

To Find :

> 1/[α+1] * [-α/β]

> - [ α/β(α+1)]

> [ 1.561 ]/[ 2.561 * - 0.561 ]

> - 1.087

This is the required answer.

_________________________________________________________