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UPSC NDA 2 2016 Mathematics Solved Paper

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Consider the following for the next two (02) items that follow:

2x^{2}+3x-\alpha-0

has roots

-2

and

\beta

while the equation

x^{2}-3mx+2m^{2}=0

has both roots positive, where

\alpha > 0

and

\beta > 0

[NDA II 2016]

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Question : 39 of 120

Marks: +1, -0

\text{ What is the value of } \alpha \text{ ? }

1/2
1
2
4

Solution:

2x^{2}+3x-\alpha=0

Its roots are

-2

and

\beta

i.e.,

\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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