InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
If `alpha,beta,gamma,sigma`are the roots of the equation `x^4+4x^3-6x^3+7x-9=0,`then he value of `(1+alpha^2)(1+beta^2)(1+gamma^2)(1+sigma^2)`is`9`b. `11`c. `13`d. 5A. 9B. 11C. 13D. 5 |
|
Answer» Correct Answer - 3 Since `alpha, beta, gamma, sigma` are the roots of the given equation, we have `x^(4) + 4x^(3) - 6x^(2) + 7x - 9 = (x - alpha)(x - beta)(x - gamma)(x - sigma)` Putting x = I and then x = -I, we get `1 - 4i + 6 + 7i - 9 = (I - alpha) (I - beta)(i - gamma) (i - sigma)` and `1 + 4i + 6 - 7i - 9 = (-i - alpha)(-i -beta)(-i -gamma)(-i - sigma)` Multiplying these two equations, we get `(-2 + 3i)(-2 - 3i) = (1 + alpha^(2))(1 + beta^(2))(1 + gamma^(2))(1 + sigma^(2))` or `13 = (1 + alpha^(2))(1 + beta^(2))(1 + gamma^(2))(1 + sigma^(2))` |
|