Number of integral values of m for which {x}^ | vedclass

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

Question

(B) Let $f(t) = t^2 + 5mt - 3m + 1$,where $t = \{x\} \in [0, 1)$.We require $f(t) < 0$ for all $t \in [0, 1)$.Since $f(t)$ is a quadratic in $t$ with

Vedclass · Accepted Answer

$0$

Vedclass · Answer

(B) Let $f(t) = t^2 + 5mt - 3m + 1$,where $t = \{x\} \in [0, 1)$.We require $f(t) Since $f(t)$ is a quadratic in $t$ with a positive leading coefficient,the parabola opens upward.For $f(t) $f(0) = -3m + 1  1 \implies m > \frac{1}{3}$.$f(1) = 1 + 5m - 3m + 1 = 2m + 2 \leq 0 \implies 2m \leq -2 \implies m \leq -1$.Combining $m > \frac{1}{3}$ and $m \leq -1$,we find no such $m$ exists.Thus,the number of integral values of $m$ is $0$.

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

Similar Questions

The set of all values of $x$ for which the inequalities $x^2-7x+10 \geq 0$ and $2x+3-x^2 > 0$ hold simultaneously is

For the inequality $2^{\log_{\sqrt{2}}(x - 1)} > x + 5$,the set of real values of $x$ is:

The number of integral values of $x$ satisfying $9 x-2 < (x+2)^2 < 12 x-3$ is

The solution of the equation $2x^2 + 3x - 9 \le 0$ is given by

If $x$ is a real number,for what values of $x$ does $3x^2 + 14x + 11 > 0$ hold?

Vedclass Test Series

Exam Paper Generator

Online Exam Module