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The quadratic equation 2x2 - 3x + 3 = 0 is to be solved numerically starting with an initial guess as x0 = 2. The new estimate of x after the first iteration using Newton-Raphson method is ________(Answer up to the nearest integer)
Correct answer is '1'. Can you explain this answer?
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Most Upvoted Answer
The quadratic equation 2x2 - 3x + 3 = 0 is to be solved numerically s...
F(x) = 2x2 - 3x + 3
⇒ f'(x) = 4x - 3
Given x = 2
New estimate of 'x' after 1st iteration,
X1 = x0 - f(x0)/f1(x0)
= 2 - f(2)/f1(2) = 2 - 5/5 = 1
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The quadratic equation 2x2 - 3x + 3 = 0 is to be solved numerically s...
Explanation:
To apply the Newton-Raphson method to solve the quadratic equation 2x^2 - 3x + 3 = 0, we need to find the root of the equation. The general formula for Newton-Raphson method is given by:
x1 = x0 - f(x0)/f'(x0)
where x0 is the initial guess, f(x) is the function we want to find the root of, and f'(x) is the derivative of the function.
First Iteration Calculation:
Given equation: 2x^2 - 3x + 3 = 0
Taking the derivative: f'(x) = 4x - 3
Plugging in x0 = 2 into the formula:
x1 = 2 - (2(2)^2 - 3(2) + 3)/(4(2) - 3)
x1 = 2 - (8 - 6 + 3)/(8 - 3)
x1 = 2 - 5/5
x1 = 2 - 1
x1 = 1
Therefore, the new estimate of x after the first iteration using the Newton-Raphson method is x = 1. The answer is rounded to the nearest integer.
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The quadratic equation 2x2 - 3x + 3 = 0 is to be solved numerically starting with an initial guess as x0 = 2. The new estimate of x after the first iteration using Newton-Raphson method is ________(Answer up to the nearest integer)Correct answer is '1'. Can you explain this answer?
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