JEE Exam  >  JEE Questions  >  If α and β (α < β) be two different real r... Start Learning for Free
If α and β (α < β) be two different real roots of the equation ax2 + bx + c = 0, then
  • a)
    α > b 2 a
  • b)
    β < b 2 a
  • c)
    α < b 2 a < β
  • d)
    β < b 2 a < α
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
If α and β (α < β) be two different real roots of the equation ax2 ...
Let f x = a x 2 + b x + c .
Then , f α = 0 = f β .
Also, f(x) is continuous and differentiable in [ α , β ] as it is a polynomial function or x.
Hence, by Rolle's theorem, there exists a k in ( α , β ), such that
f k = 0 2 a k + b = 0 k = b 2 a .
α < b 2 a < β .
View all questions of this test
Most Upvoted Answer
If α and β (α < β) be two different real roots of the equation ax2 ...
Explanation:

Given:
α and β are two different real roots of the equation ax^2 + bx + c = 0, where α < />

Proof:

1. Relationship between roots and coefficients:
For a quadratic equation ax^2 + bx + c = 0, the sum of the roots is given by -b/a and the product of the roots is given by c/a. Since α and β are the roots of the equation, we have α + β = -b/a and αβ = c/a.

2. Relationship between roots and average of roots:
The average of the roots of a quadratic equation is given by (α + β)/2. Since α < β,="" the="" average="" of="" the="" roots="" is="" closer="" to="" α="" than="" to="" />

3. Average of roots and coefficient b:
From the relationship between roots and the average of roots, we have (α + β)/2 = -b/2a. Since the average of the roots is closer to α, we can say that α < />
Therefore, the correct statement is:
α < -b/2a="" />< β.="" hence,="" option="" 'c'="" is="" the="" correct="" answer.="" β.="" hence,="" option="" 'c'="" is="" the="" correct="" />
Explore Courses for JEE exam
If α and β (α < β) be two different real roots of the equation ax2 + bx + c = 0, thena) α > − b 2 a b) β < − b 2 a c) α < − b 2 a < β d) β < − b 2 a < α Correct answer is option 'C'. Can you explain this answer?
Question Description
If α and β (α < β) be two different real roots of the equation ax2 + bx + c = 0, thena) α > − b 2 a b) β < − b 2 a c) α < − b 2 a < β d) β < − b 2 a < α Correct answer is option 'C'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If α and β (α < β) be two different real roots of the equation ax2 + bx + c = 0, thena) α > − b 2 a b) β < − b 2 a c) α < − b 2 a < β d) β < − b 2 a < α Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If α and β (α < β) be two different real roots of the equation ax2 + bx + c = 0, thena) α > − b 2 a b) β < − b 2 a c) α < − b 2 a < β d) β < − b 2 a < α Correct answer is option 'C'. Can you explain this answer?.
Solutions for If α and β (α < β) be two different real roots of the equation ax2 + bx + c = 0, thena) α > − b 2 a b) β < − b 2 a c) α < − b 2 a < β d) β < − b 2 a < α Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE. Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.
Here you can find the meaning of If α and β (α < β) be two different real roots of the equation ax2 + bx + c = 0, thena) α > − b 2 a b) β < − b 2 a c) α < − b 2 a < β d) β < − b 2 a < α Correct answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of If α and β (α < β) be two different real roots of the equation ax2 + bx + c = 0, thena) α > − b 2 a b) β < − b 2 a c) α < − b 2 a < β d) β < − b 2 a < α Correct answer is option 'C'. Can you explain this answer?, a detailed solution for If α and β (α < β) be two different real roots of the equation ax2 + bx + c = 0, thena) α > − b 2 a b) β < − b 2 a c) α < − b 2 a < β d) β < − b 2 a < α Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of If α and β (α < β) be two different real roots of the equation ax2 + bx + c = 0, thena) α > − b 2 a b) β < − b 2 a c) α < − b 2 a < β d) β < − b 2 a < α Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice If α and β (α < β) be two different real roots of the equation ax2 + bx + c = 0, thena) α > − b 2 a b) β < − b 2 a c) α < − b 2 a < β d) β < − b 2 a < α Correct answer is option 'C'. Can you explain this answer? tests, examples and also practice JEE tests.
Explore Courses for JEE exam

Top Courses for JEE

Explore Courses
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev