Number of integral values of 'm' for | vedclass

Name: PDF Generator App | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

$\{x\}^{2}+5 m\{x\}-3 m+1<0 \forall x \in R$

$f(t)=t^{2}+5 m t-3 m+1<0 \forall t \in[0,1)$

$\Rightarrow f(0)<0 \Rightarrow \mathrm{m}&g

Vedclass · Accepted Answer

$0$

Vedclass · Answer

$\{x\}^{2}+5 m\{x\}-3 m+1<0 \forall x \in R$

$f(t)=t^{2}+5 m t-3 m+1<0 \forall t \in[0,1)$

$\Rightarrow f(0)<0 \Rightarrow \mathrm{m}>\frac{1}{3}$      .......$(1)$

and $f(1)<0 \Rightarrow 2 \mathrm{m}+2<0 \Rightarrow \mathrm{m}<-1$         .......$(2)$

from $( 1)$  $\,\,\,(2) \mathrm{m} \in \phi$

Number of integral values of '$m$' for which $\{x\}^2 + 5m\{x\} - 3m + 1 < 0 $ $\forall x \in R$, is (where $\{.\}$ denotes fractional part function)

Similar Questions

If $a, b, c, d$ are four distinct numbers chosen from the set $\{1,2,3, \ldots, 9\}$, then the minimum value of $\frac{a}{b}+\frac{c}{d}$ is

If $a < 0$ then the inequality $a{x^2} - 2x + 4 > 0$ has the solution represented by

If $\alpha ,\beta ,\gamma$ are the roots of $x^3 - x - 2 = 0$, then the value of $\alpha^5 + \beta^5 + \gamma^5$ is-

How many positive real numbers $x$ satisfy the equation $x^3-3|x|+2=0$ ?

The number of distinct real roots of the equation $|\mathrm{x}+1||\mathrm{x}+3|-4|\mathrm{x}+2|+5=0$, is ...........