Let mathrm{S} be set of positive integral values of a for which frac{mathrm{ax}^2+2(mathrm{a}+1) mat

English

Gujarati

Hindi

4-2.Quadratic Equations and Inequations

hard

Let $\mathrm{S}$ be the set of positive integral values of $a$ for which $\frac{\mathrm{ax}^2+2(\mathrm{a}+1) \mathrm{x}+9 \mathrm{a}+4}{\mathrm{x}^2-8 \mathrm{x}+32}<0, \forall \mathrm{x} \in \mathbb{R}$. Then, the number of elements in $\mathrm{S}$ is :

A

$1$

B

$0$

C

$\infty$

D

$3$

(JEE MAIN-2024)

Solution

$ a x^2+2(a+1) x+9 a+4<0 \quad \forall x \in R $

$ \therefore a<0$

Standard 11

Mathematics

Share

Similar Questions

The number of real solutions of the equation $x\left(x^2+3|x|+5|x-1|+6|x-2|\right)=0$ is

hard

(JEE MAIN-2024)

Solution of the equation $\sqrt {x + 3 – 4\sqrt {x – 1} } + \sqrt {x + 8 – 6\sqrt {x – 1} } = 1$ is

normal

Below are four equations in $x$. Assume that $0 < r < 4$. Which of the following equations has the largest solution for $x$ ?

normal

(KVPY-2011)

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

normal

(KVPY-2009)

If for a posiive integer $n$ , the quadratic equation, $x\left( {x + 1} \right) + \left( {x + 1} \right)\left( {x + 2} \right) + .\;.\;.\; + \left( {x + \overline {n – 1} } \right)\left( {x + n} \right) = 10n$ has two consecutive integral solutions, then $n$ is equal to:

hard

(JEE MAIN-2017)