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Introduction

If the roots ...

Question

If the roots of the equation $x^{2} - 2 m x + m^{2} + 1 = 0$ are imaginary, then $m$ lies in

(1, \infty)

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(- \infty, \infty)

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(- \infty, 1)

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A l l o f t h e s e

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Solution

The correct option is B $(- \infty, \infty)$
$x^{2} - 2 m x + m^{2} + 1 = 0$
For roots to be imaginary
$b^{2} - 4 a c < 0$
$4 m^{2} - 4 m^{2} - 4 < 0$
$- 4 < 0$
As it is not dependent on m
So m lies $(- \infty, \infty)$

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