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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:

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

has roots -2 and

\beta

while the equation

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

has both roots positive, where

\alpha > 0

and

\beta > 0.<br><strong>Question:</strong> If \beta, 2,2 \mathrm{ m}

are in GP, then what is the value of

\beta \sqrt{\mathrm{m}}

?

Options

A $1$
B $2$
C $4$
D $6$

Correct answer

A. $1$

Step-by-step solution

\beta=\frac{1}{2}\beta, 2,2 \mathrm{ m}

are in GP.

\begin{aligned} & \Rightarrow \frac{2}{\beta}=\frac{2 m}{2} \\ & \Rightarrow \mathrm{ m}=\frac{2}{\beta}=2 \times \frac{2}{1} \\ & \Rightarrow \mathrm{ m}=4 \\ & \Rightarrow \beta \sqrt{m}=\frac{1}{2} \times \sqrt{4}=1\end{aligned}

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