TS EAMCET · Maths · Quadratic Equation
If \(f(x)\) is a polynomial of degree \(n\) with rational coefficients and \(1+2 i, 2-\sqrt{3}\) and 5 are three roots of \(f(x)=0\), then the least value of \(n\) is
- A \(5\)
- B \(4\)
- C \(3\)
- D \(6\)
Answer & Solution
Correct Answer
(A) \(5\)
Step-by-step Solution
Detailed explanation
Since, \((1+2 i),(2-\sqrt{3})\) and 5 are the some roots of polynomial \(f(x)\) of degree \(n\). As we know this conjugate are also the roots of the polynomial is, \[ (1-2 i),(2+\sqrt{3}) \] \(\therefore\) The least value of \(n\) is 5 .
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