If \(f(x) \in \mathbf{Q}[x]\) be a non-zero polynomial such that all its roots are irrational, then the…

If \(f(x) \in \mathbf{Q}[x]\) be a non-zero polynomial such that all its roots are irrational, then the degree of \(f(x)\) is
  1. an even number
  2. an odd number
  3. 0
  4. can't determine

Solution

Irrational roots exist in pair So, the degree of \(f(x)\) will be an even number

Asked in: AP EAMCET 2020 (17 Sep Shift 1)

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