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For an equation like x2 = 0 , a root exists at x = 0. The bisection method cannot be adopted to solve this equation in spite of the root existing at x = 0 because the function f (x)= x2
- a)is a polynomial
- b)has repeated roots at x = 0
- c)is always non-negative
- d)has a slope equal to zero at x = 0
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
For an equation like x2 = 0 , a root exists at x = 0. The bisection m...
Explanation:
The bisection method is an iterative numerical method used to find the root of a function within a given interval. It works by repeatedly bisecting the interval and narrowing down the search until a desired level of accuracy is achieved. However, the bisection method is only applicable when the function changes sign within the interval.
In the given equation, x^2 = 0, the function f(x) = x^2 is always non-negative. For any value of x, squaring it will result in a non-negative value. The function does not change sign within any interval, including the interval that contains the root at x = 0.
Reasoning:
- The bisection method requires the function to change sign within the interval. This is because the method relies on the intermediate value theorem, which states that if a function is continuous on a closed interval [a, b] and f(a) and f(b) have opposite signs, then the function must have at least one root within the interval.
- In the given equation, f(x) = x^2, the function is always non-negative. This means that f(a) and f(b) will have the same sign for any values of a and b, including the interval that contains the root at x = 0.
- Since the bisection method cannot guarantee convergence to the root when the function does not change sign within the interval, it cannot be used to solve the equation x^2 = 0.
Conclusion:
The bisection method cannot be adopted to solve the equation x^2 = 0 because the function f(x) = x^2 is always non-negative and does not change sign within any interval, including the interval that contains the root at x = 0. The method requires the function to change sign within the interval, which is not satisfied in this case. Therefore, an alternative method, such as the Newton-Raphson method or the fixed-point iteration method, should be used to solve the equation.
The bisection method is an iterative numerical method used to find the root of a function within a given interval. It works by repeatedly bisecting the interval and narrowing down the search until a desired level of accuracy is achieved. However, the bisection method is only applicable when the function changes sign within the interval.
In the given equation, x^2 = 0, the function f(x) = x^2 is always non-negative. For any value of x, squaring it will result in a non-negative value. The function does not change sign within any interval, including the interval that contains the root at x = 0.
Reasoning:
- The bisection method requires the function to change sign within the interval. This is because the method relies on the intermediate value theorem, which states that if a function is continuous on a closed interval [a, b] and f(a) and f(b) have opposite signs, then the function must have at least one root within the interval.
- In the given equation, f(x) = x^2, the function is always non-negative. This means that f(a) and f(b) will have the same sign for any values of a and b, including the interval that contains the root at x = 0.
- Since the bisection method cannot guarantee convergence to the root when the function does not change sign within the interval, it cannot be used to solve the equation x^2 = 0.
Conclusion:
The bisection method cannot be adopted to solve the equation x^2 = 0 because the function f(x) = x^2 is always non-negative and does not change sign within any interval, including the interval that contains the root at x = 0. The method requires the function to change sign within the interval, which is not satisfied in this case. Therefore, an alternative method, such as the Newton-Raphson method or the fixed-point iteration method, should be used to solve the equation.
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Community Answer
For an equation like x2 = 0 , a root exists at x = 0. The bisection m...
Since f(x) = x2 will never be negative , the statement f(xu)f(xℓ)<0 will="" never="" be="">
Therefore, no interval [xℓ, xu] will contain the root of x2 = 0.
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For an equation like x2 = 0 , a root exists at x = 0. The bisection method cannot be adopted to solve this equation in spite of the root existing at x = 0 because the function f (x)= x2 a)is a polynomialb)has repeated roots at x = 0c)is always non-negatived)has a slope equal to zero at x = 0Correct answer is option 'C'. Can you explain this answer?
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For an equation like x2 = 0 , a root exists at x = 0. The bisection method cannot be adopted to solve this equation in spite of the root existing at x = 0 because the function f (x)= x2 a)is a polynomialb)has repeated roots at x = 0c)is always non-negatived)has a slope equal to zero at x = 0Correct answer is option 'C'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about For an equation like x2 = 0 , a root exists at x = 0. The bisection method cannot be adopted to solve this equation in spite of the root existing at x = 0 because the function f (x)= x2 a)is a polynomialb)has repeated roots at x = 0c)is always non-negatived)has a slope equal to zero at x = 0Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For an equation like x2 = 0 , a root exists at x = 0. The bisection method cannot be adopted to solve this equation in spite of the root existing at x = 0 because the function f (x)= x2 a)is a polynomialb)has repeated roots at x = 0c)is always non-negatived)has a slope equal to zero at x = 0Correct answer is option 'C'. Can you explain this answer?.
For an equation like x2 = 0 , a root exists at x = 0. The bisection method cannot be adopted to solve this equation in spite of the root existing at x = 0 because the function f (x)= x2 a)is a polynomialb)has repeated roots at x = 0c)is always non-negatived)has a slope equal to zero at x = 0Correct answer is option 'C'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about For an equation like x2 = 0 , a root exists at x = 0. The bisection method cannot be adopted to solve this equation in spite of the root existing at x = 0 because the function f (x)= x2 a)is a polynomialb)has repeated roots at x = 0c)is always non-negatived)has a slope equal to zero at x = 0Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For an equation like x2 = 0 , a root exists at x = 0. The bisection method cannot be adopted to solve this equation in spite of the root existing at x = 0 because the function f (x)= x2 a)is a polynomialb)has repeated roots at x = 0c)is always non-negatived)has a slope equal to zero at x = 0Correct answer is option 'C'. Can you explain this answer?.
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