Math Problem Statement
Find real root of the equation x^2-5x-7=0 which lies between 2and 3 correct to four decimal places
Solution
We are tasked with finding the real root of the equation that lies between 2 and 3, correct to four decimal places.
We can solve this equation using the Bisection Method, which is a numerical method for finding roots of continuous functions. Since we know that the root lies between 2 and 3, we can apply this method iteratively to approximate the root.
Steps of the Bisection Method:
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Initial Interval: Start with the interval , where and .
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Midpoint: Compute the midpoint of the interval:
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Function Evaluation: Evaluate the function at the midpoint .
If , then is the root. -
Interval Update: If and have opposite signs, the root lies in , so we set . If and have opposite signs, the root lies in , so we set .
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Repeat the Process: Continue narrowing the interval by updating and until the difference between and is sufficiently small (i.e., until the approximation reaches four decimal places).
Let me calculate the root step by step using the Bisection Method.
Iterative Steps:
- Interval [2, 3]:
Since the two values give same negative signs, move to next
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Math Problem Analysis
Mathematical Concepts
Algebra
Root-Finding
Numerical Methods
Bisection Method
Formulas
x^2 - 5x - 7 = 0
Theorems
Bisection Method for Root-Finding
Suitable Grade Level
Grades 10-12