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NDA 2013
Exam
NDA
Year
2013
Subject
Mathematics
Chapter
Quadratic Equation

NDA 2013 · Mathematics · Quadratic Equation

If α, β are the roots of the equation a x^2+b x+b=0 , then what is...

If α,β\alpha, \beta are the roots of the equation ax2+bx+b=0a x^2+b x+b=0, then what is the value of αβ+βα+ba\sqrt{\frac{\alpha}{\beta}}+\sqrt{\frac{\beta}{\alpha}}+\sqrt{\frac{b}{a}} ?

Options

  1. A–1
  2. B0
  3. C1
  4. D2

Correct answer

B. 0

Step-by-step solution

αβ+βα+ba=α+βα⋅β+ba\sqrt{\frac{\alpha}{\beta}}+\sqrt{\frac{\beta}{\alpha}}+\sqrt{\frac{b}{a}}=\frac{\alpha+\beta}{\sqrt{\alpha \cdot \beta}}+\sqrt{\frac{b}{a}} Sum of roots of given equation ax2+bx+b=0α+β=−baa x^2+b x+b=0\alpha+\beta=-\frac{b}{a} so, −baba+ba=−ba+ba=0\frac{-\frac{b}{a}}{\sqrt{\frac{b}{a}}}+\sqrt{\frac{b}{a}}=-\sqrt{\frac{b}{a}}+\sqrt{\frac{b}{a}}=0
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