Question

To remove the second term of the equation $x^4-8x^3+x^2-x+3=0$, diminish the root of the equation by

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

The correct option is B $2$

Suppose the roots of the equation are $\alpha ,\beta ,\gamma$ and $\delta$

"we have to remove the second term of the equation means the sum of the roots should be zero"

In this equation sum of the roots is

$\alpha +$ $\beta +$ $\gamma +$ $\delta =8$

Now we can see if we subtract $2$ from each roots, then the sum of the roots will be zero

$\Rightarrow$ $(\alpha -2)+$ $(\beta -2)+$ $(\gamma -2)+$ $(\delta -2)=8-8=0$

So we can conclude that if we diminish the roots of the equation by two then the second term of the equation will be removed.

Hence, option B is correct.