solve x^3 - 2x - 5 =0 by using Cardan's method
Answers
Answer:
F(x) = x3-2x-5
Polynomial Roots Calculator is a set of methods aimed at finding values of x for which F(x)=0
Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers x which can be expressed as the quotient of two integers
The Rational Root Theorem states that if a polynomial zeroes for a rational number P/Q then P is a factor of the Trailing Constant and Q is a factor of the Leading Coefficient
In this case, the Leading Coefficient is 1 and the Trailing Constant is -5.
The factor(s) are:
of the Leading Coefficient : 1
of the Trailing Constant : 1 ,5
Let us test ....
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