CA Foundation Exam > CA Foundation Questions > The solution of the cubic equation x3-6x2+11x...
Start Learning for Free
The solution of the cubic equation x3-6x2+11x-6=0 is given by the triplet:
- a)(-1, 1, -2)
- b)(1, 2, 3)
- c)(-2, 2, 3)
- d)(0, 4, -5)
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
The solution of the cubic equation x3-6x2+11x-6=0 is given by the trip...
Ans.
Given (x^3)-6(x^2)+11x-6=0
x^3-3x^2-3x^2+11x-6=0
x^2(x-3)-(3x^2-11x+6)=0
x^2(x-3)-(3x^2-9x-2x+6)=0
x^2(x-3)-(3x(x-3)-2(x-3))=0
x^2(x-3)-[(x-3)(3x-2)]=0
(x-3)(x^2-3x+2)=0
(x-3)(x^2-2x-x+2)=0
(x-3)(x(x-2)-1(x-2))=0
(x-3)(x-2)(x-1)=0
x^3-3x^2-3x^2+11x-6=0
x^2(x-3)-(3x^2-11x+6)=0
x^2(x-3)-(3x^2-9x-2x+6)=0
x^2(x-3)-(3x(x-3)-2(x-3))=0
x^2(x-3)-[(x-3)(3x-2)]=0
(x-3)(x^2-3x+2)=0
(x-3)(x^2-2x-x+2)=0
(x-3)(x(x-2)-1(x-2))=0
(x-3)(x-2)(x-1)=0
This question is part of UPSC exam. View all CA Foundation courses
Most Upvoted Answer
The solution of the cubic equation x3-6x2+11x-6=0 is given by the trip...
Solution:
The given cubic equation is x3-6x2+11x-6=0.
To solve this equation, we can use the Rational Root Theorem and synthetic division method.
Rational Root Theorem states that if a polynomial equation has integer coefficients, then any rational root of the equation must have the form p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.
In this case, the constant term is -6 and the leading coefficient is 1. So, the possible rational roots are ±1, ±2, ±3, ±6.
We can check each of these roots using synthetic division and see which one gives us a remainder of 0.
Using synthetic division with x=2, we get:
2 | 1 -6 11 -6
| 2 -8 6
|----------
| 1 -4 3 0
Since we get a remainder of 0, x=2 is a root of the equation.
Now, we can use the Factor Theorem to factor the equation as:
x3-6x2+11x-6 = (x-2)(x2-4x+3)
We can then solve the quadratic equation x2-4x+3=0 using the quadratic formula or factoring:
x2-4x+3=0
(x-3)(x-1)=0
x=1 or x=3
Therefore, the solution of the cubic equation x3-6x2+11x-6=0 is given by the triplet (-2, 2, 3).
Hence, the correct answer is option 'C'.
The given cubic equation is x3-6x2+11x-6=0.
To solve this equation, we can use the Rational Root Theorem and synthetic division method.
Rational Root Theorem states that if a polynomial equation has integer coefficients, then any rational root of the equation must have the form p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.
In this case, the constant term is -6 and the leading coefficient is 1. So, the possible rational roots are ±1, ±2, ±3, ±6.
We can check each of these roots using synthetic division and see which one gives us a remainder of 0.
Using synthetic division with x=2, we get:
2 | 1 -6 11 -6
| 2 -8 6
|----------
| 1 -4 3 0
Since we get a remainder of 0, x=2 is a root of the equation.
Now, we can use the Factor Theorem to factor the equation as:
x3-6x2+11x-6 = (x-2)(x2-4x+3)
We can then solve the quadratic equation x2-4x+3=0 using the quadratic formula or factoring:
x2-4x+3=0
(x-3)(x-1)=0
x=1 or x=3
Therefore, the solution of the cubic equation x3-6x2+11x-6=0 is given by the triplet (-2, 2, 3).
Hence, the correct answer is option 'C'.
Community Answer
The solution of the cubic equation x3-6x2+11x-6=0 is given by the trip...
A square and an equilateral triangle have equal perimeter if the diagonal of the square is9√2 cm then area of the triangle is
|
|
Explore Courses for CA Foundation exam
|
|
Similar CA Foundation Doubts
Top Courses for CA FoundationView all
The solution of the cubic equation x3-6x2+11x-6=0 is given by the triplet:a)(-1, 1, -2)b)(1, 2, 3)c)(-2, 2, 3)d)(0, 4, -5)Correct answer is option 'C'. Can you explain this answer?
Question Description
The solution of the cubic equation x3-6x2+11x-6=0 is given by the triplet:a)(-1, 1, -2)b)(1, 2, 3)c)(-2, 2, 3)d)(0, 4, -5)Correct answer is option 'C'. Can you explain this answer? for CA Foundation 2025 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about The solution of the cubic equation x3-6x2+11x-6=0 is given by the triplet:a)(-1, 1, -2)b)(1, 2, 3)c)(-2, 2, 3)d)(0, 4, -5)Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for CA Foundation 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The solution of the cubic equation x3-6x2+11x-6=0 is given by the triplet:a)(-1, 1, -2)b)(1, 2, 3)c)(-2, 2, 3)d)(0, 4, -5)Correct answer is option 'C'. Can you explain this answer?.
The solution of the cubic equation x3-6x2+11x-6=0 is given by the triplet:a)(-1, 1, -2)b)(1, 2, 3)c)(-2, 2, 3)d)(0, 4, -5)Correct answer is option 'C'. Can you explain this answer? for CA Foundation 2025 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about The solution of the cubic equation x3-6x2+11x-6=0 is given by the triplet:a)(-1, 1, -2)b)(1, 2, 3)c)(-2, 2, 3)d)(0, 4, -5)Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for CA Foundation 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The solution of the cubic equation x3-6x2+11x-6=0 is given by the triplet:a)(-1, 1, -2)b)(1, 2, 3)c)(-2, 2, 3)d)(0, 4, -5)Correct answer is option 'C'. Can you explain this answer?.
Solutions for The solution of the cubic equation x3-6x2+11x-6=0 is given by the triplet:a)(-1, 1, -2)b)(1, 2, 3)c)(-2, 2, 3)d)(0, 4, -5)Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for CA Foundation.
Download more important topics, notes, lectures and mock test series for CA Foundation Exam by signing up for free.
Here you can find the meaning of The solution of the cubic equation x3-6x2+11x-6=0 is given by the triplet:a)(-1, 1, -2)b)(1, 2, 3)c)(-2, 2, 3)d)(0, 4, -5)Correct answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
The solution of the cubic equation x3-6x2+11x-6=0 is given by the triplet:a)(-1, 1, -2)b)(1, 2, 3)c)(-2, 2, 3)d)(0, 4, -5)Correct answer is option 'C'. Can you explain this answer?, a detailed solution for The solution of the cubic equation x3-6x2+11x-6=0 is given by the triplet:a)(-1, 1, -2)b)(1, 2, 3)c)(-2, 2, 3)d)(0, 4, -5)Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of The solution of the cubic equation x3-6x2+11x-6=0 is given by the triplet:a)(-1, 1, -2)b)(1, 2, 3)c)(-2, 2, 3)d)(0, 4, -5)Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The solution of the cubic equation x3-6x2+11x-6=0 is given by the triplet:a)(-1, 1, -2)b)(1, 2, 3)c)(-2, 2, 3)d)(0, 4, -5)Correct answer is option 'C'. Can you explain this answer? tests, examples and also practice CA Foundation tests.
|
|
Explore Courses for CA Foundation exam
|
|
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