Question

If alpha and beta are the zeroes of the polynomial x2+4x+3, find the polynomial where zeroes are 1+beta /alpha and 1+alpha / beta

Answer 1

Answer:

x^2-2x=0

Step-by-step explanation:

Step-by-step explanation:

First of all, factorize the given polynomial:

x^2+4x+3=0\\(x+3)(x+1)=0\\x=-3\:\:or\:\:x=-1

Let the -3 be the α, and the -1 be the β.

It is required to find the polynomials which have the roots of:

x=\frac{1+\beta}{\alpha} and x=\frac{1+\alpha}{\beta}.

Substitute by α=-3, and β=-1:

Therefore, the roots are: x = 0 and x = 2

Therefore, the polynomial must be: x(x-2)=0

Polynomial: x^2-2x=0