(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 2 Complex Numbers and Quadratic Equations: Quadratic Equations 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

2 Complex Numbers and Quadratic Equations: Quadratic Equations

Subtopic

Quadratic expressions and Position of roots

Previous Year

JEE MAIN 2023 Paper All JEE MAIN years →

Number of integral values of $a$ for which both roots of the quadratic equation $x^2 - (2a + 3)x + a^2 + 3a = 0$ lie in the interval $(0, 4)$ is:

View Solution

If $f(x) = \frac{1}{4x^2 + 2x + 1}$,then its maximum value is

Medium

View Solution

If $\alpha$ and $\beta$ are the roots of the quadratic equation $ax^2 + bx + c = 0$ and $k$ is a real number,then the condition for $\alpha < k < \beta$ is given by:

Easy

View Solution

Let $a, b, c$ be real numbers such that $a+b+c < 0$ and the quadratic equation $a x^{2}+b x+c=0$ has imaginary roots. Then:

EasyWBJEE 2019

View Solution

If $y = f(x) = ax^2 + 2bx + c = 0$ has imaginary roots and $4a + 4b + c < 0$,then :-

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

Number of integral values of $a$ for which both roots of the quadratic equation $x^2 - (2a + 3)x + a^2 + 3a = 0$ lie in the interval $(0, 4)$ is:

If $f(x) = \frac{1}{4x^2 + 2x + 1}$,then its maximum value is

If $\alpha$ and $\beta$ are the roots of the quadratic equation $ax^2 + bx + c = 0$ and $k$ is a real number,then the condition for $\alpha < k < \beta$ is given by:

Let $a, b, c$ be real numbers such that $a+b+c < 0$ and the quadratic equation $a x^{2}+b x+c=0$ has imaginary roots. Then:

If $y = f(x) = ax^2 + 2bx + c = 0$ has imaginary roots and $4a + 4b + c < 0$,then :-

Vedclass Test Series

Exam Paper Generator

Online Exam Module