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NDA 2020
Exam
NDA
Year
2020
Subject
Mathematics
Chapter
Quadratic Equation

NDA 2020 · Mathematics · Quadratic Equation

If α and β are the roots of the equation x^2-3 x+2=0 , then what is...

If cot⁡α\cot \alpha and cot⁡β\cot \beta are the roots of the equation x2−3x+2=0x^2-3 x+2=0, then what is cot⁡(α+β)\cot (\alpha+\beta) equal to ?

Options

  1. A12\frac{1}{2}
  2. B13\frac{1}{3}
  3. C2
  4. D3

Correct answer

B. 13\frac{1}{3}

Step-by-step solution

Given equation: x2−3x+2=0x^2-3 x+2=0 Sum of roots, cot⁡α+cot⁡β=−(−3)=3\cot \alpha+\cot \beta=-(-3)=3 (i) Product of roots, cot⁡α⋅cot⁡β=2\cot \alpha \cdot \cot \beta=2 (ii) Now, cot⁡(α+β)=cot⁡α⋅cot⁡β−1cot⁡α+cot⁡β=2−13=13\cot (\alpha+\beta)=\frac{\cot \alpha \cdot \cot \beta-1}{\cot \alpha+\cot \beta}=\frac{2-1}{3}=\frac{1}{3}.
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