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UPSC NDA I 2012 Mathematics Paper

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For the next Two (2) questions that follow:

The equation formed by multiplying each root of

a x^2+b x

+c=0

by 2 is

x^2+36 x+24=0

.

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Question : 23 of 120

Marks: +1, -0

What is

b:c

$3:1$
$1:2$
$1:3$
$3:2$

Solution:

Let

\alpha, \beta

be roots of equation

a x^2+b x+c \;\; =0

\therefore \;\; \alpha+\beta \;\; =\frac{-b}{a}

\alpha\beta \;\; =\frac{c}{a}

So,

2\alpha

and

2\beta

we roots of equation

x^2+36x+24 \;\; =0

2\alpha+2\beta \;\; =-36

\alpha+\beta \;\; =-18

\Rightarrow \;\; \frac{-b}{a} \;\; =-18 \Rightarrow b=18a

(2\alpha)+(2\beta) \;\; =24

\alpha\beta \;\; =6

\frac{c}{a} \;\; =6 \Rightarrow c=6a

\therefore b:c=3:1

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