AP EAMCET · Maths · Complex Number
If \(3+i\) and \(2-\sqrt{3}\) are the roots of the equation \(\mathrm{f}(\mathrm{x})=\mathrm{a}_0+\mathrm{a}_1 \mathrm{x}+\mathrm{a}_2 \mathrm{x}^2+\ldots .+\mathrm{a}_{\mathrm{n}} \mathrm{x}^{\mathrm{n}} ; \mathrm{a}_0, \mathrm{a}_1 \ldots . . \mathrm{a}_{\mathrm{n}} \in \mathbb{Z}\), then the least value of \(\mathrm{n}\) and value of \(\mathrm{a}_0\) are respectively.
- A 4,1
- B 4,10
- C 4,-10
- D 4,-1
Answer & Solution
Correct Answer
(B) 4,10
Step-by-step Solution
Detailed explanation
Given \(f(x)=a_0+a_1 x+a_2 x^2+\ldots+a_n x^n, a_0, a_1, a_2\), \(\ldots a_n \in Z\). ...(i) Since \((3+i)\) and \((2-\sqrt{3})\) are roots of equation (i) Hence \((3-i)\) and \((2+\sqrt{3})\) will also be the roots of given equation. Therefore, now we have at least 4 roots of…
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