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TS EAMCET · Maths · Functions

Assertion (A) If \(a_1, a_2, \ldots, a_n\) are the \(n\) distinct roots of the equation \(x^n-2=0\), then \(1+\left(1-a_1\right)\left(1-a_2\right) \ldots\left(1-a_{n-1}\right)\left(1-a_n\right)=0\) Reason (R) If \(\alpha_1, \alpha_2, \ldots, \alpha_n\) are the roots of \(f(x) \equiv p_0 x^n+p_1 x^{n-1}+p_2 x^{n-2}+\ldots+p_n=0\), then the roots of \(f(g(x))=0 \operatorname{are~}^{-1}\left(\alpha_i\right), i=1,2,3, \ldots, n\) The correct option among the following is

  1. A (A) is true, (R) is true and (R) is the correct explanation for (A).
  2. B (A) is true, (R) is true but (R) is not the correct explanation for (A).
  3. C (A) is true but (R) is false .
  4. D (A) is false but (R) is true.
Verified Solution

Answer & Solution

Correct Answer

(A) (A) is true, (R) is true and (R) is the correct explanation for (A).

Step-by-step Solution

Detailed explanation

Given, \(a_1, a_2, a_3, \ldots, a_n\) are \(n\) distinct roots of…
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