CAT Exam > CAT Questions > What is the condition for one root of the qua...
Start Learning for Free
What is the condition for one root of the quadratic equation ax^2 bx c=0 to be twice the other?
Most Upvoted Answer
What is the condition for one root of the quadratic equation ax^2 bx ...
Condition for One Root of a Quadratic Equation to be Twice the Other
A quadratic equation is an equation of the form ax^2 + bx + c = 0, where a, b, and c are constants and x is the variable. The solutions to this equation are the values of x that make the equation true. If the discriminant (b^2 - 4ac) is negative, there are no real solutions to the equation. If the discriminant is zero, there is one real solution to the equation. If the discriminant is positive, there are two real solutions to the equation.
General Form of Quadratic Equation
The general form of a quadratic equation is ax^2 + bx + c = 0, where a, b, and c are constants.
Roots of Quadratic Equation
The roots of a quadratic equation are the values of x that make the equation true. There can be two, one or no real solutions.
Condition for One Root to be Twice the Other
If the roots of a quadratic equation are α and β, and α is twice β, then:
α + β = -b/a
αβ = c/a
Let α = 2β, then:
2β + β = -b/a
β = -b/3a
αβ = c/a
2β^2 = c/a
β^2 = c/2a
Substituting the value of β in the second equation:
(-b/3a)^2 = c/2a
b^2 - 12ac = 0
Therefore, the condition for one root of the quadratic equation ax^2 + bx + c = 0 to be twice the other is b^2 - 4ac = 0.
Community Answer
What is the condition for one root of the quadratic equation ax^2 bx ...
Let roots are p and q
say p=2q
p+q=-b/a
3q=-b/a....(1)
p.q=c/a
2q^2=c/a...(2)
from. 1 and 2
(b)^2/9(a)^2 = c/2a
2ab^2=9ca^2
b^2=(9/2)ca
say p=2q
p+q=-b/a
3q=-b/a....(1)
p.q=c/a
2q^2=c/a...(2)
from. 1 and 2
(b)^2/9(a)^2 = c/2a
2ab^2=9ca^2
b^2=(9/2)ca
Attention CAT Students!
To make sure you are not studying endlessly, EduRev has designed CAT study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in CAT.
|
Explore Courses for CAT exam
|
|
Similar CAT Doubts
Top Courses for CATView all
What is the condition for one root of the quadratic equation ax^2 bx c=0 to be twice the other?
Question Description
What is the condition for one root of the quadratic equation ax^2 bx c=0 to be twice the other? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about What is the condition for one root of the quadratic equation ax^2 bx c=0 to be twice the other? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the condition for one root of the quadratic equation ax^2 bx c=0 to be twice the other?.
What is the condition for one root of the quadratic equation ax^2 bx c=0 to be twice the other? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about What is the condition for one root of the quadratic equation ax^2 bx c=0 to be twice the other? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the condition for one root of the quadratic equation ax^2 bx c=0 to be twice the other?.
Solutions for What is the condition for one root of the quadratic equation ax^2 bx c=0 to be twice the other? in English & in Hindi are available as part of our courses for CAT.
Download more important topics, notes, lectures and mock test series for CAT Exam by signing up for free.
Here you can find the meaning of What is the condition for one root of the quadratic equation ax^2 bx c=0 to be twice the other? defined & explained in the simplest way possible. Besides giving the explanation of
What is the condition for one root of the quadratic equation ax^2 bx c=0 to be twice the other?, a detailed solution for What is the condition for one root of the quadratic equation ax^2 bx c=0 to be twice the other? has been provided alongside types of What is the condition for one root of the quadratic equation ax^2 bx c=0 to be twice the other? theory, EduRev gives you an
ample number of questions to practice What is the condition for one root of the quadratic equation ax^2 bx c=0 to be twice the other? tests, examples and also practice CAT tests.
|
|
Explore Courses for CAT exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup