Question

if alpha and beta are the zeros of polynomial x2 +4x +3,find the polynomial whose zeroes are 1 +beta divide alpha and 1 +alpha divide beta.

Answer 1

Answer:

$x^2-2x=0$

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: $x^2-2x=0$

Answer 2

this is the correct answer