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

English

Gujarati

Hindi

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

Share

Similar Questions

The number of distinct real roots of the equation $x^{5}\left(x^{3}-x^{2}-x+1\right)+x\left(3 x^{3}-4 x^{2}-2 x+4\right)-1=0$ is

normal

(JEE MAIN-2022)

Let $a, b, c$ be non-zero real roots of the equation $x^3+a x^2+b x+c=0$. Then,

normal

(KVPY-2020)

If $\alpha ,\,\beta ,\,\gamma $ are the roots of the equation ${x^3} + 4x + 1 = 0,$ then ${(\alpha + \beta )^{ – 1}} + {(\beta + \gamma )^{ – 1}} + {(\gamma + \alpha )^{ – 1}} = $

medium

The number of solutions for the equation ${x^2} – 5|x| + \,6 = 0$ is

easy

If $\alpha ,\beta,\gamma$ are the roots of equation $x^3 + 2x -5 = 0$ and if equation $x^3 + bx^2 + cx + d = 0$ has roots $2 \alpha + 1, 2 \beta + 1, 2 \gamma + 1$ , then value of $|b + c + d|$ is (where $b,c,d$ are coprime)-

normal