(D) Since $(x-2)$ is a common factor of the expressions $x^2+ax+b$ and $x^2+cx+d$,the value of these expressions at $x=2$ must be $0$.For $x^2+ax+b$:

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

(D) Since $(x-2)$ is a common factor of the expressions $x^2+ax+b$ and $x^2+cx+d$,the value of these expressions at $x=2$ must be $0$.For $x^2+ax+b$: $(2)^2+a(2)+b=0 \Rightarrow 4+2a+b=0 \dots(i)$For $x^2+cx+d$: $(2)^2+c(2)+d=0 \Rightarrow 4+2c+d=0 \dots(ii)$Subtracting equation $(ii)$ from equation $(i)$:$(4+2a+b) - (4+2c+d) = 0 - 0$$2a+b-2c-d = 0$$b-d = 2c-2a$$b-d = 2(c-a)$Dividing both sides by $(c-a)$ (assuming $c \neq a$):$\frac{b-d}{c-a} = 2$

Class 11 Mathematics 4-2.Quadratic Equations and Inequations Solution of quadratic equations and Nature of roots

Difficult

If $(x-2)$ is a common factor of the expressions $x^2+ax+b$ and $x^2+cx+d$,then $\frac{b-d}{c-a}$ is equal to

AP EAMCET 2004 All AP EAMCET

TS EAMCET 2004 All TS EAMCET

A
$-2$
B
$-1$
C
$1$
D
$2$

Explore More

Browse All

Question Bank

All Subjects

Class 11 Questions

Class 11

Mathematics Questions

Chapter

4-2.Quadratic Equations and Inequations

Subtopic

Solution of quadratic equations and Nature of roots

Previous Year

AP EAMCET 2004 Paper All AP EAMCET years →

Previous Year

TS EAMCET 2004 Paper All TS EAMCET years →

If $\alpha$ and $\beta$ are roots of the equation $x^2 - x + 1 = 0$,then $\alpha^{2009} + \beta^{2009} = \dots$

DifficultAIEEE 2010

View Solution

To remove the second term of the equation $x^4-8x^3+x^2-x+3=0$,diminish the roots of the equation by

DifficultAP EAMCET 2002

View Solution

If $a, b, c$ are distinct and the roots of $(b-c)x^2 + (c-a)x + (a-b) = 0$ are equal,then $a, b$ and $c$ are in

EasyAP EAMCET 2015

View Solution

When $b=17$,it is found that the roots of the equation $x^2+bx+c=0$ are $-2$ and $-15$. If $\alpha, \beta$ are the roots of the same equation when $b=13$,then $|\alpha-\beta|=$

EasyTS EAMCET 2022

View Solution

Let $a$ be an integer selected at random from the set $\{0, 1, 2, 3, ..., 9\}$. The probability that the equation $ax^2 - ax + 1 = 0$ has real roots is ...

DifficultMHT CET 2026

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

If $(x-2)$ is a common factor of the expressions $x^2+ax+b$ and $x^2+cx+d$,then $\frac{b-d}{c-a}$ is equal to

Similar Questions

If $\alpha$ and $\beta$ are roots of the equation $x^2 - x + 1 = 0$,then $\alpha^{2009} + \beta^{2009} = \dots$

To remove the second term of the equation $x^4-8x^3+x^2-x+3=0$,diminish the roots of the equation by

If $a, b, c$ are distinct and the roots of $(b-c)x^2 + (c-a)x + (a-b) = 0$ are equal,then $a, b$ and $c$ are in

When $b=17$,it is found that the roots of the equation $x^2+bx+c=0$ are $-2$ and $-15$. If $\alpha, \beta$ are the roots of the same equation when $b=13$,then $|\alpha-\beta|=$

Let $a$ be an integer selected at random from the set $\{0, 1, 2, 3, ..., 9\}$. The probability that the equation $ax^2 - ax + 1 = 0$ has real roots is ...

Vedclass Test Series

Exam Paper Generator

Online Exam Module