Q. 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 $\alpha_{i},\ \ i = 1,\ 2,\ 3,\ 4.$ Now, $x$ is replaced by $x - 1$, now roots of new equation are
A) $\frac{1}{\alpha_{i} + 1\ },i = 1,\ 2,\ 3,\ 4$
B) $\alpha_{i} + 1,\ i = 1,\ 2,\ 3,\ 4$
C) $\alpha_{i} - 1,i = 1,\ 2,\ 3,\ 4$
D) None of these
Explanation
(b)
Now, $x - 1 = \alpha_{i}\ \Rightarrow x = \alpha_{i} + 1$ for new equation, $i = 1,\ 2,\ 3,\ 4$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.