Find a root of the equation x³-5x-7 that lies between 2 and 3
using
Regula-Falsi Method correct up to four decimal pla

2 thoughts on “Find a root of the equation x³-5x-7 that lies between 2 and 3 <br />using <br />Regula-Falsi Method correct up to four decimal pla”

1. Answer:

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2. Given:–

   • x³ – 2x – 5 = 0

   To Find:–

   • root of the equation by Bisection method correct up to three decimal places

   Solution:–

   x³ – 2x – 5 = 0

   • x = 1 => 1 – 2 – 5 = – 6

   • x = 2 => 8 – 4 – 5 = – 1

   • x = 3 => 27 – 6 – 5 = 16

   0 lies between -1 & 16

   Hence x lies between 2 & 3

   • (2 + 3)/2 = 2.5

   • x = 2.5 => x³ – 2x – 5 = 5.625

   0 lies between -1 & 5.625

   • => x lies between 2 & 2.5

   • (2 + 2.5)/2 = 2.25

   • x = 2.25 => x³ – 2x – 5 = 1.89

   0 lies between -1 & 1.89

   • => x lies between 2 & 2.25

   • => x = 2.125 => x³ – 2x – 5 = 0.34

   0 lies between -1 & 0.34

   • => x lies between 2 × 2.125

   • => x = 2.0625 => x³ – 2x – 5 = -0.35

   0 lies between -0.35 & 0.34

   • => x lies between 2.0625 & 2.125

   • x = 2.09375 => x³ – 2x – 5 = -0.0089 ≈ 0

   • x = 2.094 up to three decimal places

   x = 2.094

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   →Show the function f of x is equal to x cube minus 3 x square + 6 x …

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