Question

Remove the second term from the equation:
$x^4+4x^3+2x^2-4x-2=0$.

Answer 1

Given, $x^4+4x^3+2x^2-4x-2=0$

There are 4 roots of the equation as it has a degree of 4. Let’s say $a,b,c$ and $d$

Sum of the roots = -4

To eliminate the $2^{nd}$ term we need sum of the roots should be $0$ which can be achieved by increasing each root of the given equation by 1.

$\therefore$ The we need to find the equation with roots $a+1,b+1,c+1$ and $d+1$

Transformed equation by inputting $x=x-1$ is $(x-1{)}^4+4(x-1{)}^3+2(x-1{)}^2-4(x-1)-2=0$

$⟹x^4–4x^2+4x+1=0$