# Use Regula False Method to Find the Real Root of the Equation

by Ansar
(Paksitan)

use regula false method to find the real root of the equation

x^3-sinx +1=0

correct to four decimal places after three succesive approximation is (-2,-1)

Note : all the calculation should be done in radian mode only.

### Comments for Use Regula False Method to Find the Real Root of the Equation

 Oct 20, 2011 Regula Falsi Method to Find the Real Root of the Equation by: Staff ----------------------------------------------------------- Part II -60 . . . . . . .-1.0472 . . . . . . . .-1.14838 . . . . . . .-0.86602 . . . . . . .0.717647 -61 . . . . . . .-1.06465 . . . . . . .-1.20676 . . . . . . .-0.87462 . . . . . . .0.66786 -62 . . . . . . .-1.0821 . . . . . . . .-1.26709 . . . . . . .-0.88295 . . . . . . .0.615861 -63 . . . . . . .-1.09956 . . . . . . .-1.32939 . . . . . . .-0.89101 . . . . . . .0.561615 -64 . . . . . . .-1.11701 . . . . . . .-1.39371 . . . . . . .-0.89879 . . . . . . .0.505088 -65 . . . . . . .-1.13446 . . . . . . .-1.46006 . . . . . . .-0.90631 . . . . . . .0.446246 -66 . . . . . . .-1.15192 . . . . . . .-1.52849 . . . . . . .-0.91355 . . . . . . .0.385054 -67 . . . . . . .-1.16937 . . . . . . .-1.59903 . . . . . . .-0.9205 . . . . . . . .0.321479 -68 . . . . . . .-1.18682 . . . . . . .-1.6717 . . . . . . . .-0.92718 . . . . . . .0.255486 -69 . . . . . . .-1.20428 . . . . . . .-1.74654 . . . . . . .-0.93358 . . . . . . .0.187041 -70 . . . . . . .-1.22173 . . . . . . .-1.82358 . . . . . . .-0.93969 . . . . . . .0.116111 -71 . . . . . . .-1.23918 . . . . . . .-1.90286 . . . . . . .-0.94552 . . . . . . .0.042662 -72 . . . . . . .-1.25664 . . . . . . .-1.9844 . . . . . . . .-0.95106 . . . . . . .-0.03334 -73 . . . . . . .-1.27409 . . . . . . .-2.06823 . . . . . . .-0.9563 . . . . . . . .-0.11193 -74 . . . . . . .-1.29154 . . . . . . .-2.1544 . . . . . . . .-0.96126 . . . . . . .-0.19314 -75 . . . . . . .-1.309 . . . . . . . . .-2.24293 . . . . . . .-0.96593 . . . . . . .-0.277 -76 . . . . . . .-1.32645 . . . . . . .-2.33384 . . . . . . .-0.9703 . . . . . . . .-0.36355 -77 . . . . . . .-1.3439 . . . . . . . .-2.42719 . . . . . . .-0.97437 . . . . . . .-0.45282 -78 . . . . . . .-1.36136 . . . . . . .-2.52299 . . . . . . .-0.97815 . . . . . . .-0.54484 -79 . . . . . . .-1.37881 . . . . . . .-2.62127 . . . . . . .-0.98163 . . . . . . .-0.63965 -80 . . . . . . .-1.39626 . . . . . . .-2.72208 . . . . . . .-0.98481 . . . . . . .-0.73727 -81 . . . . . . .-1.41372 . . . . . . .-2.82544 . . . . . . .-0.98769 . . . . . . .-0.83775 -82 . . . . . . .-1.43117 . . . . . . .-2.93138 . . . . . . .-0.99027 . . . . . . .-0.94112 As you can see, the solution to the equation x³ - sin(x) +1 = 0 occurs when x ≈ -1.24 radians (about -71.5 degrees) you can see a graph of this function by opening the link shown below (1) If your browser is Firefox, click the following link to VIEW; or if your browser is Chrome, Internet Explorer, Opera, or Safari (2A) highlight and copy the link, then (2B) paste the link into your browser Address bar & press enter: Use the Backspace key to return to this page http://www.solving-math-problems.com/images/graph-function-2011-10-19.png Thanks for writing. Staff www.solving-math-problems.com

 Oct 20, 2011 Regula Falsi Method to Find the Real Root of the Equation by: Staff Part I Question: by Ansar (Pakistan) use regula false method to find the real root of the equation x^3-sinx +1=0 correct to four decimal places after three successive approximation is (-2,-1) Note : all the calculation should be done in radian mode only. Answer: The Regula Falsi method is a trial and error method of solving equations. It is also called the “guess and check” method. Test values are substituted for variables in an equation to see which values work. x³ - sinx +1 = 0 You can use excel to generate as many calculations as you need. These are some of the figures I used: column 1: x in degrees column 2: x in radians = x*3.14159/180 column 3: x^3 using x in radians column 4: sin(x) using x in radians column 5: x^3 – sin(x) +1 , using x in radians -----------------------------------------------------------