(C) Let $f(x) = 2x^2 - 8x + k$.For one root to lie in $(1,2)$ and the other in $(2,3)$,the value of the quadratic at $x=2$ must be negative,and the va

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

(C) Let $f(x) = 2x^2 - 8x + k$.For one root to lie in $(1,2)$ and the other in $(2,3)$,the value of the quadratic at $x=2$ must be negative,and the values at $x=1$ and $x=3$ must be positive.$f(1) = 2(1)^2 - 8(1) + k = k - 6 > 0 \implies k > 6$.$f(3) = 2(3)^2 - 8(3) + k = 18 - 24 + k = k - 6 > 0 \implies k > 6$.$f(2) = 2(2)^2 - 8(2) + k = 8 - 16 + k = k - 8 Combining these,we get $6 The only integral value of $k$ in this interval is $k = 7$.

Class 11 Mathematics 4-2.Quadratic Equations and Inequations Quadratic expressions and Position of roots

Difficult

The number of integral values of $k$,for which one root of the equation $2x^2-8x+k=0$ lies in the interval $(1,2)$ and its other root lies in the interval $(2,3)$,is:

JEE MAIN 2023 All JEE MAIN

A
$2$
B
$0$
C
$1$
D
$3$

Explore More

Browse All

Question Bank

All Subjects

Class 11 Questions

Class 11

Mathematics Questions

Chapter

4-2.Quadratic Equations and Inequations

Subtopic

Quadratic expressions and Position of roots

Previous Year

JEE MAIN 2023 Paper All JEE MAIN years →

If $\alpha, \beta$ are the roots of $x^2+bx+c=0$,$\gamma, \delta$ are the roots of $x^2+b_1x+c_1=0$ and $\gamma < \alpha < \delta < \beta$,then $(c-c_1)^2 < $

DifficultAP EAMCET 2019

View Solution

If the maximum value of $2x - 7 - ax^2$ cannot exceed $20$,then the minimum value of $a$ is

EasyTS EAMCET 2019

View Solution

If $c > 0$ and the equation $3ax^2 + 4bx + c = 0$ has no real root,then :-

View Solution

The quadratic expression $(2x+1)^{2} - px + q \neq 0$ for any real $x$, if

MediumWBJEE 2015

View Solution

If $f(x) = x^2 + 2bx + 2c^2$ and $g(x) = -x^2 - 2cx + b^2$ such that $\min f(x) > \max g(x)$,then the relation between $b$ and $c$ is

DifficultIIT 2003

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

The number of integral values of $k$,for which one root of the equation $2x^2-8x+k=0$ lies in the interval $(1,2)$ and its other root lies in the interval $(2,3)$,is:

Similar Questions

If $\alpha, \beta$ are the roots of $x^2+bx+c=0$,$\gamma, \delta$ are the roots of $x^2+b_1x+c_1=0$ and $\gamma < \alpha < \delta < \beta$,then $(c-c_1)^2 < $

If the maximum value of $2x - 7 - ax^2$ cannot exceed $20$,then the minimum value of $a$ is

If $c > 0$ and the equation $3ax^2 + 4bx + c = 0$ has no real root,then :-

The quadratic expression $(2x+1)^{2} - px + q \neq 0$ for any real $x$, if

If $f(x) = x^2 + 2bx + 2c^2$ and $g(x) = -x^2 - 2cx + b^2$ such that $\min f(x) > \max g(x)$,then the relation between $b$ and $c$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module