Class 10 Exam > Class 10 Questions > find the zeroes of the polynomial f of x ...
Start Learning for Free
find the zeroes of the polynomial f of x = x cube -12×Sq +39× - 28 ,if it is given that the zeroes are in AP.
?
Most Upvoted Answer
find the zeroes of the polynomial f of x = x cube -12×Sq +39× ...
Community Answer
find the zeroes of the polynomial f of x = x cube -12×Sq +39× ...
Finding the Zeroes of the Polynomial
To find the zeroes of the polynomial f(x) = x³ - 12x² + 39x - 28, given that the zeroes are in Arithmetic Progression (AP), follow these steps:
Step 1: Understanding Zeroes in AP
- Let the zeroes be a - d, a, and a + d.
- The sum of the zeroes can be represented as: (a - d) + a + (a + d) = 3a.
Step 2: Applying Vieta's Formulas
- According to Vieta's formulas, the sum of the zeroes is equal to the coefficient of x² (with opposite sign):
- 3a = 12, hence a = 4.
Step 3: Finding the Zeroes
- The zeroes can now be expressed as:
- 4 - d, 4, and 4 + d.
- The product of the zeroes (from Vieta's) is given by:
- (4 - d) * 4 * (4 + d) = 28.
Step 4: Simplifying the Product
- Expanding the equation:
- (16 - d²) * 4 = 28
- 64 - 4d² = 28
- 4d² = 36
- d² = 9, thus d = 3 or d = -3.
Step 5: Final Zeroes
- Therefore, the zeroes are:
- 4 - 3 = 1,
- 4,
- 4 + 3 = 7.
Conclusion
- The zeroes of the polynomial f(x) = x³ - 12x² + 39x - 28 are:
- 1, 4, 7, which are indeed in AP.
To find the zeroes of the polynomial f(x) = x³ - 12x² + 39x - 28, given that the zeroes are in Arithmetic Progression (AP), follow these steps:
Step 1: Understanding Zeroes in AP
- Let the zeroes be a - d, a, and a + d.
- The sum of the zeroes can be represented as: (a - d) + a + (a + d) = 3a.
Step 2: Applying Vieta's Formulas
- According to Vieta's formulas, the sum of the zeroes is equal to the coefficient of x² (with opposite sign):
- 3a = 12, hence a = 4.
Step 3: Finding the Zeroes
- The zeroes can now be expressed as:
- 4 - d, 4, and 4 + d.
- The product of the zeroes (from Vieta's) is given by:
- (4 - d) * 4 * (4 + d) = 28.
Step 4: Simplifying the Product
- Expanding the equation:
- (16 - d²) * 4 = 28
- 64 - 4d² = 28
- 4d² = 36
- d² = 9, thus d = 3 or d = -3.
Step 5: Final Zeroes
- Therefore, the zeroes are:
- 4 - 3 = 1,
- 4,
- 4 + 3 = 7.
Conclusion
- The zeroes of the polynomial f(x) = x³ - 12x² + 39x - 28 are:
- 1, 4, 7, which are indeed in AP.
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
find the zeroes of the polynomial f of x = x cube -12×Sq +39× - 28 ,if it is given that the zeroes are in AP. Related: Video: Introduction to Polynomials (Detailed)?
Question Description
find the zeroes of the polynomial f of x = x cube -12×Sq +39× - 28 ,if it is given that the zeroes are in AP. Related: Video: Introduction to Polynomials (Detailed)? 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 find the zeroes of the polynomial f of x = x cube -12×Sq +39× - 28 ,if it is given that the zeroes are in AP. Related: Video: Introduction to Polynomials (Detailed)? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for find the zeroes of the polynomial f of x = x cube -12×Sq +39× - 28 ,if it is given that the zeroes are in AP. Related: Video: Introduction to Polynomials (Detailed)?.
find the zeroes of the polynomial f of x = x cube -12×Sq +39× - 28 ,if it is given that the zeroes are in AP. Related: Video: Introduction to Polynomials (Detailed)? 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 find the zeroes of the polynomial f of x = x cube -12×Sq +39× - 28 ,if it is given that the zeroes are in AP. Related: Video: Introduction to Polynomials (Detailed)? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for find the zeroes of the polynomial f of x = x cube -12×Sq +39× - 28 ,if it is given that the zeroes are in AP. Related: Video: Introduction to Polynomials (Detailed)?.
Solutions for find the zeroes of the polynomial f of x = x cube -12×Sq +39× - 28 ,if it is given that the zeroes are in AP. Related: Video: Introduction to Polynomials (Detailed)? 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 find the zeroes of the polynomial f of x = x cube -12×Sq +39× - 28 ,if it is given that the zeroes are in AP. Related: Video: Introduction to Polynomials (Detailed)? defined & explained in the simplest way possible. Besides giving the explanation of
find the zeroes of the polynomial f of x = x cube -12×Sq +39× - 28 ,if it is given that the zeroes are in AP. Related: Video: Introduction to Polynomials (Detailed)?, a detailed solution for find the zeroes of the polynomial f of x = x cube -12×Sq +39× - 28 ,if it is given that the zeroes are in AP. Related: Video: Introduction to Polynomials (Detailed)? has been provided alongside types of find the zeroes of the polynomial f of x = x cube -12×Sq +39× - 28 ,if it is given that the zeroes are in AP. Related: Video: Introduction to Polynomials (Detailed)? theory, EduRev gives you an
ample number of questions to practice find the zeroes of the polynomial f of x = x cube -12×Sq +39× - 28 ,if it is given that the zeroes are in AP. Related: Video: Introduction to Polynomials (Detailed)? 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
|
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