If α 1,α 2,α 3,α 4 are the roots of the equation x4+(2-√3)x2+2+√3=0, then the value of (1-α 1)(1-α 2)(1-α 3)(1-α 4) is:

Question

If α 1,α 2,α 3,α 4 are the roots of the equation x4+(2-√3)x2+2+√3=0, then the value of (1-α 1)(1-α 2)(1-α 3)(1-α 4) is: (A) 1 (B) 4 (C)  2+√3  (D) 5

Tardigrade Admin · Accepted Answer

(1-α 1)(1-α 2)(1-α 3)(1-α 4) =(1+α 1α 2-α 1-α 2)(1-α 3)(1-α 4) =(1+α 1α 2-α 1-α 2-α 3-α 1α 2α 3 +α 1α 3+α 2α 3)(1-α 4) =1+ Sigma α 1α 2- Sigma α 1α 2α 3- Sigma α 1+α 1α 2α 3α 4 =1+(2-√3)-0-0+2+√3 =-2√3+1+2+√3=5

Q. If $α_{1}, α_{2}, α_{3}, α_{4}$ are the roots of the equation $x^{4} + (2 - 3) x^{2} + 2 + 3 = 0,$ then the value of $(1 - α_{1}) (1 - α_{2}) (1 - α_{3}) (1 - α_{4})$ is:

1

4

$2 + 3$

5

0

Q. If α1​,α2​,α3​,α4​ are the roots of the equation x4+(2−3​)x2+2+3​=0, then the value of (1−α1​)(1−α2​)(1−α3​)(1−α4​) is:

1

4

2+3​

5

0

Q. If $α_{1}, α_{2}, α_{3}, α_{4}$ are the roots of the equation $x^{4} + (2 - 3) x^{2} + 2 + 3 = 0,$ then the value of $(1 - α_{1}) (1 - α_{2}) (1 - α_{3}) (1 - α_{4})$ is:

$2 + 3$