Question

The transformed equation of $x^3+6x^2+12x-19=0$ by eliminating second term, is:

• A. $x^3+3x-27=0$
• B. $x^3-3x+27=0$
• C. $x^3+27=0$
• D. $x^3-27=0$

Answer 1

Answer: (D)

$x^3-27=0$

Given equation is $x^3+6x^2+12x-19=0$

For removing the second order term let us replace $x$ by $x+k$,

$(x+k{)}^3+6(x+k{)}^2+12(x+k)-19$

$x^3+3x{k}^2+3x^{2}k+k^3+6(x^2+2kx+k^2)+12x+12k-19$

Coefficient of $x^2$ is $(3k+6)$ which must be equal to zero .

So, we get the $k=-2$

So, our equation becomes $x^3-27$ when we put $k=-2$ .