Number of positive integral values of 'K' for which equation k = left| {x + left| {2x

English

Gujarati

Hindi

4-2.Quadratic Equations and Inequations

normal

Number of positive integral values of $'K'$ for which the equation $k = \left| {x + \left| {2x - 1} \right|} \right| - \left| {x - \left| {2x - 1} \right|} \right|$ has exactly three real solutions, is

A

$0$

B

$2$

C

$3$

D

$5$

Solution

$\left| {x + \left| {2x – 1} \right|} \right| – \left| {x – \left| {2x – 1} \right|} \right| = 2Min\left( {x,\left| {2x – 1} \right|} \right)$

$|2 x-1|=x$

$\therefore 2 x-1=\pm x$

$x=1, \frac{1}{3}$

at $x=\frac{1}{3}$

$\mathrm{k}=\left|\frac{1}{3}+\frac{1}{3}\right|=\frac{2}{3}$

Standard 11

Mathematics

Share

Similar Questions

The equation $\sqrt {3 {x^2} + x + 5} = x – 3$ , where $x$ is real, has

hard

(JEE MAIN-2014)

The number of real solutions of the equation $\mathrm{x}|\mathrm{x}+5|+2|\mathrm{x}+7|-2=0$ is …………………

hard

(JEE MAIN-2024)

Consider a three-digit number with the following properties:

$I$. If its digits in units place and tens place are interchanged, the number increases by $36$ ;

$II.$ If its digits in units place and hundreds place are interchanged, the number decreases by $198 .$

Now, suppose that the digits in tens place and hundreds place are interchanged. Then, the number

normal

(KVPY-2017)

If $x$ is real and satisfies $x + 2 > \sqrt {x + 4} ,$ then

medium

Let $p_1(x)=x^3-2020 x^2+b_1 x+c_1$ and $p_2(x)=x^3-2021 x^2+b_2 x+c_2$ be polynomials having two common roots $\alpha$ and $\beta$. Suppose there exist polynomials $q_1(x)$ and $q_2(x)$ such that $p_1(x) q_1(x)+p_2(x) q_2(x)=x^2-3 x+2$. Then the correct identity is

normal

(KVPY-2020)