Question

if alpha and beta are the zeroes of the polynomialx2-4x+3​

Answer 1

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Your question is not completed so,i think your question is,

${Q.}$ If alpha and beta are the zeros of polynomial ${x}^{2} +4x +3$find the polynomial whose zeroes are 1 +beta divide alpha and 1 +alpha divide beta.

Then,

$\huge\bold\red{{solution:-}}$

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.

Therefore,

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 ${x = 2}$

The polynomial must be: ${x(x-2)=0}$

Polynomial=${x}{^2}-{2x=0}$

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