Number of roots of equation log ( - 2x) = 2log (x + 1) are

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4-2.Quadratic Equations and Inequations

easy

The number of roots of the equation $\log ( - 2x)$ $ = 2\log (x + 1)$ are

A

$3$

B

$2$

C

$1$

D

None of these

Solution

(b) Given , $\log ( – 2x) = 2\log (x + 1)$

$ \Rightarrow – 2x = {(x + 1)^2}$ $ \Rightarrow {x^2} + 4x + 1 = 0$

==> $x = \frac{{ – 4 \pm \sqrt {16 – 4} }}{2}$ ==> $x = \frac{{ – 4 \pm \sqrt {12} }}{2}$

==> $x = – 2 \pm \sqrt 3 $==> $x = ( – 2 + \sqrt 3 ),( – 2 – \sqrt 3 )$.

Standard 11

Mathematics

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