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NDA 2018
Exam
NDA
Year
2018
Subject
Mathematics
Chapter
Quadratic Equation

NDA 2018 · Mathematics · Quadratic Equation

If α and β(0 < α < β < ) are the roots of the quadratic equation 4...

If cos⁡α\cos \alpha and cos⁡β(0<α<β<)\cos \beta(0 < \alpha < \beta < ) are the roots of the quadratic equation 4x2−3=04 x^2-3=0, then what is the value of sec⁡α×sec⁡β\sec \alpha \times \sec \beta ?

Options

  1. A−43-\frac{4}{3}
  2. B43\frac{4}{3}
  3. C34\frac{3}{4}
  4. D−34-\frac{3}{4}

Correct answer

A. −43-\frac{4}{3}

Step-by-step solution

 Product of roots =ca⇒cos⁡α⋅cos⁡β=−34⇒1cos⁡α⋅cos⁡β=sec⁡α⋅sec⁡β=−43\begin{aligned} & \text{ Product of roots }=\frac{\mathrm{c}}{\mathrm{a}} \\ & \Rightarrow \cos \alpha \cdot \cos \beta=-\frac{3}{4} \\ & \Rightarrow \frac{1}{\cos \alpha \cdot \cos \beta}=\sec \alpha \cdot \sec \beta=-\frac{4}{3}\end{aligned}
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