JEE Exam > JEE Questions > Product of real roots of the equation t2x2+|x...
Start Learning for Free
Product of real roots of the equation t2x2+|x|+9=0 [2002]
- a)is always positive
- b)is always negative
- c)does not exist
- d)none of these
Correct answer is option 'A'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
Product of real roots of the equation t2x2+|x|+9=0 [2002]a)is always p...
Product of real roots = 
∴ Product of real roots is always positive.
Most Upvoted Answer
Product of real roots of the equation t2x2+|x|+9=0 [2002]a)is always p...
**Answer:**
To solve the equation t^2 * x^2 * |x| - 9 = 0, we can break it down into two cases: when x is positive and when x is negative.
**Case 1: x is positive**
In this case, the equation becomes t^2 * x^3 - 9 = 0. Solving for x, we have:
x^3 = 9/t^2
Taking the cube root of both sides, we get:
x = (9/t^2)^(1/3)
Since t^2 is always positive, the cube root of (9/t^2) will also be positive. Therefore, the product of the real roots in this case will be positive.
**Case 2: x is negative**
In this case, the equation becomes t^2 * x^3 + 9 = 0. Solving for x, we have:
x^3 = -9/t^2
Taking the cube root of both sides, we get:
x = -(9/t^2)^(1/3)
Again, since t^2 is always positive, the cube root of (-9/t^2) will also be positive. However, the negative sign in front of the cube root makes x negative. Therefore, the product of the real roots in this case will be negative.
Since the product of the real roots is positive in both cases, we can conclude that the product of the real roots is always positive. Therefore, the correct answer is option 'A'.
To solve the equation t^2 * x^2 * |x| - 9 = 0, we can break it down into two cases: when x is positive and when x is negative.
**Case 1: x is positive**
In this case, the equation becomes t^2 * x^3 - 9 = 0. Solving for x, we have:
x^3 = 9/t^2
Taking the cube root of both sides, we get:
x = (9/t^2)^(1/3)
Since t^2 is always positive, the cube root of (9/t^2) will also be positive. Therefore, the product of the real roots in this case will be positive.
**Case 2: x is negative**
In this case, the equation becomes t^2 * x^3 + 9 = 0. Solving for x, we have:
x^3 = -9/t^2
Taking the cube root of both sides, we get:
x = -(9/t^2)^(1/3)
Again, since t^2 is always positive, the cube root of (-9/t^2) will also be positive. However, the negative sign in front of the cube root makes x negative. Therefore, the product of the real roots in this case will be negative.
Since the product of the real roots is positive in both cases, we can conclude that the product of the real roots is always positive. Therefore, the correct answer is option 'A'.
Attention JEE Students!
To make sure you are not studying endlessly, EduRev has designed JEE study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in JEE.
|
Explore Courses for JEE exam
|
|
Similar JEE Doubts
Top Courses for JEEView all
Product of real roots of the equation t2x2+|x|+9=0 [2002]a)is always positiveb)is always negativec)does not existd)none of theseCorrect answer is option 'A'. Can you explain this answer?
Question Description
Product of real roots of the equation t2x2+|x|+9=0 [2002]a)is always positiveb)is always negativec)does not existd)none of theseCorrect answer is option 'A'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Product of real roots of the equation t2x2+|x|+9=0 [2002]a)is always positiveb)is always negativec)does not existd)none of theseCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Product of real roots of the equation t2x2+|x|+9=0 [2002]a)is always positiveb)is always negativec)does not existd)none of theseCorrect answer is option 'A'. Can you explain this answer?.
Product of real roots of the equation t2x2+|x|+9=0 [2002]a)is always positiveb)is always negativec)does not existd)none of theseCorrect answer is option 'A'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Product of real roots of the equation t2x2+|x|+9=0 [2002]a)is always positiveb)is always negativec)does not existd)none of theseCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Product of real roots of the equation t2x2+|x|+9=0 [2002]a)is always positiveb)is always negativec)does not existd)none of theseCorrect answer is option 'A'. Can you explain this answer?.
Solutions for Product of real roots of the equation t2x2+|x|+9=0 [2002]a)is always positiveb)is always negativec)does not existd)none of theseCorrect answer is option 'A'. 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 Product of real roots of the equation t2x2+|x|+9=0 [2002]a)is always positiveb)is always negativec)does not existd)none of theseCorrect answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Product of real roots of the equation t2x2+|x|+9=0 [2002]a)is always positiveb)is always negativec)does not existd)none of theseCorrect answer is option 'A'. Can you explain this answer?, a detailed solution for Product of real roots of the equation t2x2+|x|+9=0 [2002]a)is always positiveb)is always negativec)does not existd)none of theseCorrect answer is option 'A'. Can you explain this answer? has been provided alongside types of Product of real roots of the equation t2x2+|x|+9=0 [2002]a)is always positiveb)is always negativec)does not existd)none of theseCorrect answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Product of real roots of the equation t2x2+|x|+9=0 [2002]a)is always positiveb)is always negativec)does not existd)none of theseCorrect answer is option 'A'. Can you explain this answer? tests, examples and also practice JEE tests.
|
|
Explore Courses for JEE 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