Class 10 Exam > Class 10 Questions > If 2/3 is root of quadratic equation kx² - Q ...
Start Learning for Free
If 2/3 is root of quadratic equation kx² - Q - 2 is equals to zero then find the value of k?
Most Upvoted Answer
If 2/3 is root of quadratic equation kx² - Q - 2 is equals to zero the...
Understanding the Problem
To solve for \( k \) in the quadratic equation \( kx^2 - Q - 2 = 0 \) with \( \frac{2}{3} \) as a root, we will substitute \( x = \frac{2}{3} \) into the equation.
Substituting the Root
1. Substitute \( x = \frac{2}{3} \) into the equation:
\[
k\left(\frac{2}{3}\right)^2 - Q - 2 = 0
\]
2. Calculate \( \left(\frac{2}{3}\right)^2 \):
- \( \left(\frac{2}{3}\right)^2 = \frac{4}{9} \)
3. Substitute back:
\[
k \cdot \frac{4}{9} - Q - 2 = 0
\]
Rearranging the Equation
4. Rearranging gives us:
\[
k \cdot \frac{4}{9} = Q + 2
\]
5. To isolate \( k \), multiply both sides by \( \frac{9}{4} \):
\[
k = \frac{9(Q + 2)}{4}
\]
Conclusion
Thus, the value of \( k \) depends on the value of \( Q \). For various values of \( Q \), you can find the corresponding \( k \) using:
\[
k = \frac{9(Q + 2)}{4}
\]
This formula allows you to compute \( k \) whenever \( Q \) is provided.
To solve for \( k \) in the quadratic equation \( kx^2 - Q - 2 = 0 \) with \( \frac{2}{3} \) as a root, we will substitute \( x = \frac{2}{3} \) into the equation.
Substituting the Root
1. Substitute \( x = \frac{2}{3} \) into the equation:
\[
k\left(\frac{2}{3}\right)^2 - Q - 2 = 0
\]
2. Calculate \( \left(\frac{2}{3}\right)^2 \):
- \( \left(\frac{2}{3}\right)^2 = \frac{4}{9} \)
3. Substitute back:
\[
k \cdot \frac{4}{9} - Q - 2 = 0
\]
Rearranging the Equation
4. Rearranging gives us:
\[
k \cdot \frac{4}{9} = Q + 2
\]
5. To isolate \( k \), multiply both sides by \( \frac{9}{4} \):
\[
k = \frac{9(Q + 2)}{4}
\]
Conclusion
Thus, the value of \( k \) depends on the value of \( Q \). For various values of \( Q \), you can find the corresponding \( k \) using:
\[
k = \frac{9(Q + 2)}{4}
\]
This formula allows you to compute \( k \) whenever \( Q \) is provided.
Attention Class 10 Students!
To make sure you are not studying endlessly, EduRev has designed Class 10 study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Class 10.
|
Explore Courses for Class 10 exam
|
|
Similar Class 10 Doubts
Top Courses for Class 10View all
If 2/3 is root of quadratic equation kx² - Q - 2 is equals to zero then find the value of k?
Question Description
If 2/3 is root of quadratic equation kx² - Q - 2 is equals to zero then find the value of k? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about If 2/3 is root of quadratic equation kx² - Q - 2 is equals to zero then find the value of k? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If 2/3 is root of quadratic equation kx² - Q - 2 is equals to zero then find the value of k?.
If 2/3 is root of quadratic equation kx² - Q - 2 is equals to zero then find the value of k? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about If 2/3 is root of quadratic equation kx² - Q - 2 is equals to zero then find the value of k? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If 2/3 is root of quadratic equation kx² - Q - 2 is equals to zero then find the value of k?.
Solutions for If 2/3 is root of quadratic equation kx² - Q - 2 is equals to zero then find the value of k? in English & in Hindi are available as part of our courses for Class 10.
Download more important topics, notes, lectures and mock test series for Class 10 Exam by signing up for free.
Here you can find the meaning of If 2/3 is root of quadratic equation kx² - Q - 2 is equals to zero then find the value of k? defined & explained in the simplest way possible. Besides giving the explanation of
If 2/3 is root of quadratic equation kx² - Q - 2 is equals to zero then find the value of k?, a detailed solution for If 2/3 is root of quadratic equation kx² - Q - 2 is equals to zero then find the value of k? has been provided alongside types of If 2/3 is root of quadratic equation kx² - Q - 2 is equals to zero then find the value of k? theory, EduRev gives you an
ample number of questions to practice If 2/3 is root of quadratic equation kx² - Q - 2 is equals to zero then find the value of k? tests, examples and also practice Class 10 tests.
|
|
Explore Courses for Class 10 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
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup