Question

In the equation $a_4{x}^4+a_3{x}^3+a_2{x}^2+a_{1}x+a_0=0$ roots of the equation are $a_1,i=1,2,3,4$ Now x is replaced by x-1. Roots of new equation are:

• A. $\frac{1}{{\alpha }_1+1},i=1,2,3,4$
• B. ${\alpha }_1+1,i=1,2,3,4$
• C. ${\alpha }_1-1,i=1,2,3,4$
• D. $noneofthese$

Answer 1

Answer: (B)

${\alpha }_1+1,i=1,2,3,4$

$a_4{x}^4+a_3{x}^4+a_2{x}^2+a_{1}x+a_0=0$

if x is replaced by x-1, then,

$a_4(1-x{)}^4+a_3(x-1{)}^3+a_2(x-1{)}^2+a_1(x-1)+a_0=0$

extra terms will be $a_4+a_3+a_2+a_1+a_0$

so new roots will be

$\alpha i+1,i=1,2,3,4$