(A) Given that $a, b, c$ are in Arithmetic Progression $(AP)$,we have $2b = a + c$. Substituting this into the quadratic equation $ax^2 - 2bx + c = 0$

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

(A) Given that $a, b, c$ are in Arithmetic Progression $(AP)$,we have $2b = a + c$. Substituting this into the quadratic equation $ax^2 - 2bx + c = 0$,we get: $ax^2 - (a + c)x + c = 0$ $ax^2 - ax - cx + c = 0$ $ax(x - 1) - c(x - 1) = 0$ $(x - 1)(ax - c) = 0$ Thus,the roots are $x = 1$ and $x = \frac{c}{a}$. Hence,option $A$ is correct.

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

Easy

If $a, b, c$ are in Arithmetic Progression $(AP)$,then the roots of the equation $ax^2 - 2bx + c = 0$ are

AP EAMCET 2020 All AP EAMCET

A
$1, \frac{c}{a}$
B
$\frac{-1}{a}, -c$
C
$-1, \frac{-c}{a}$
D
$-2, \frac{-c}{2a}$

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 2020 Paper All AP EAMCET years →

The number of real roots of the equation $\frac{(x^2+1)^3}{x^3} + \frac{x^2+1}{3x} = 0, (x \neq 0)$ is

MediumAP EAMCET 2021

View Solution

The roots of $|x - 2|^2 + |x - 2| - 6 = 0$ are

Medium

View Solution

If the roots of $x^2 - bx + c = 0$ are two consecutive integers,then $b^2 - 4c$ is

MediumAIEEE 2005

View Solution

If ${b_1}{b_2} = 2({c_1} + {c_2})$,then at least one of the equations ${x^2} + {b_1}x + {c_1} = 0$ and ${x^2} + {b_2}x + {c_2} = 0$ has

Medium

View Solution

If $x$ is real,then the minimum value of ${x^2} - 8x + 17$ is

Easy

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 $a, b, c$ are in Arithmetic Progression $(AP)$,then the roots of the equation $ax^2 - 2bx + c = 0$ are

Similar Questions

The number of real roots of the equation $\frac{(x^2+1)^3}{x^3} + \frac{x^2+1}{3x} = 0, (x \neq 0)$ is

The roots of $|x - 2|^2 + |x - 2| - 6 = 0$ are

If the roots of $x^2 - bx + c = 0$ are two consecutive integers,then $b^2 - 4c$ is

If ${b_1}{b_2} = 2({c_1} + {c_2})$,then at least one of the equations ${x^2} + {b_1}x + {c_1} = 0$ and ${x^2} + {b_2}x + {c_2} = 0$ has

If $x$ is real,then the minimum value of ${x^2} - 8x + 17$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module