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NDA 2016
Exam
NDA
Year
2016
Subject
Mathematics
Chapter
Quadratic Equation

NDA 2016 · Mathematics · Quadratic Equation

Paragraph: 2 x^2+3 x-α-0 has roots -2 and β while the equation...

Paragraph: 2x2+3x−α−02 x^2+3 x-\alpha-0 has roots -2 and β\beta while the equation x2−3mx+2m2=0x^2-3 \mathrm{mx}+2 \mathrm{ m}^2=0 has both roots positive, where α>0\alpha > 0 and β>0.<br><strong>Question:</strong>Whatisthevalueofα\beta > 0.<br><strong>Question:</strong> What is the value of \alpha ?

Options

  1. A1/21 / 2
  2. B11
  3. C22
  4. D44

Correct answer

C. 22

Step-by-step solution

2x2+3x−α=02 x^2+3 x-\alpha=0 Its roots are: −2  and β-2 \ \text{ and } \beta. i.e., −32=β−2⇒β=2−32=12⇒β=12α2=2β⇒α=4×12⇒α=2\frac{-3}{2}=\beta-2 \Rightarrow \beta=2-\frac{3}{2}=\frac{1}{2} \Rightarrow \beta=\frac{1}{2}\frac{\alpha}{2}=2 \beta \Rightarrow \alpha=4 \times \frac{1}{2} \Rightarrow \alpha=2
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