Question

The transformed equations of $x^3-6x^2+5x+8=0$ by eliminating second term is

• A. $x^3+7x+2=0$
• B. $x^3-7x+2=0$
• C. $x^3+5x+2=0$
• D. $x^3-5x+2=0$

Answer 1

The correct option is B $x^3-7x+2=0$

To eliminate the second term from the equation $x^3-6x^2+5x+8=0$......(1) let us use the substitution $x+h$ in place of $x$ in (1).

The we have,

$(x+h{)}^3-6(x+h{)}^2+5(x+h)+8=0$

or, $(x^3+3x^{2}h+3x{h}^2+h^3)-6(x^2+2xh+h^2)+5(x+h)+8=0$

or, $x^3+x^2(3h-6)+x(3h^2-12h+5)+(h^3-6h^2+5h+8)=0$......(2)

To eliminate the second term from the equation we mus have $3h-6=0\Rightarrow h=2$.

Putting $h=2$ in (2) we get,

$x^3-7x+2=0$.

So option (B) is correct.