Question

Remove the second term from the equation:
$x^6-12x^5+3x^2-17x+300=0$.

Answer 1

$f\left(x\right)=x^6-12x^5+3x^2-17x+300=0$

There are 6 roots of the equation and sum of the roots is $12$, hence to eliminate the 2^nd term we need to the reduce sum to zero.

Hence, we need to decrease each of the roots of the $f\left(x\right)=0$ by 2

Transform the equation by inputting $x=x+2$

$(x+2{)}^6-12(x+2{)}^5+3(x+2{)}^2-17(x+2)+300=0$

$⟹x^6-60x^4-320x^3-717x^2-773x-42=0$