Let [t] denote greatest integer ≤ t . Then equation in x ,[ x ]^{2}+2[ x +2]-7=0 has

English

Gujarati

Hindi

4-2.Quadratic Equations and Inequations

medium

Let $[t]$ denote the greatest integer $\leq t .$ Then the equation in $x ,[ x ]^{2}+2[ x +2]-7=0$ has

A

no integral solution

B

exactly four integral solutions

C

exactly two solutions

D

infinitely many solutions

(JEE MAIN-2020)

Solution

$[x]^{2}+2[x+2]-7=0$

$\Rightarrow[x]^{2}+2[x]+4-7=0$

$\Rightarrow[x]=1,-3$

$\Rightarrow x \in[1,2) \cup[-3,-2)$

Standard 11

Mathematics

Share

Similar Questions

Number of solutions of equation $|x^2 -2|x||$ = $2^x$ , is

normal

The number of real roots of the equation, $\mathrm{e}^{4 \mathrm{x}}+\mathrm{e}^{3 \mathrm{x}}-4 \mathrm{e}^{2 \mathrm{x}}+\mathrm{e}^{\mathrm{x}}+1=0$ is

hard

(JEE MAIN-2020)

If graph of $y = ax^2 -bx + c$ is following, then sign of $a$, $b$, $c$ are

normal

The sum of all the roots of the equation $\left|x^2-8 x+15\right|-2 x+7=0$ is:

hard

(JEE MAIN-2023)

Let $y = \sqrt {\frac{{(x + 1)(x – 3)}}{{(x – 2)}}} $, then all real values of $x$ for which $y$ takes real values, are

hard

(IIT-1980)