Question

Find the equation when the roots of the equation $x^5-4x^4+3x^2-4x+6=0$ is diminished by $3$.

Answer 1

$f\left(x\right)=x^5-4x^4+3x^2-4x+6=0$

$y=x-3⟹x=y+3$

$⟹f\left(y\right)=(y+3{)}^5-4(y+3{)}^4+3(y+3{)}^2-4(y+3)+6=0$

$⟹f\left(y\right)=y^5+11y^4+78y^3+219y^2+311y-60=0$