Question

X4-x-10=0 equation solve using bisection method solution

Answer 1

Answer:

Step by step solution :

Step 1:

Polynomial Roots Calculator :

1.1 Find roots (zeroes) of : F(x) = x4-x-10

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 -10.

The factor(s) are:

of the Leading Coefficient : 1

of the Trailing Constant : 1 ,2 ,5 ,10

Step 2 :

Quadratic equations:

2.1 Solve x4-x-10 = 0

In search of an interavl at which the above polynomial changes sign, from negative to positive or the other wayaround.

Method of search: Calculate polynomial values for all integer points between x=-20 and x=+20

Found change of sign between x= -2.00 and x= -1.00

Approximating a root using the Bisection Method :

We now use the Bisection Method to approximate one of the solutions. The Bisection Method is an iterative procedure to approximate a root (Root is another name for a solution of an equation).

The function is F(x) = x4 - x - 10

At x= -1.00 F(x) is equal to -8.00

At x= -2.00 F(x) is equal to 8.00

Intuitively we feel, and justly so, that since F(x) is negative on one side of the interval, and positive on the other side then, somewhere inside this interval, F(x) is zero.

x = -1.697471857

Answer 2

Answer:

x = -1.697471857

Step-by-step explanation:

Stage 1:

Polynomial Roots Calculator :

1.1 Find roots (zeroes) of :  $F(x) = x^{4} - x -10$

Polynomial Roots Calculator is a bunch of techniques pointed toward tracking down upsides of $x$  for which  $F(x) = 0$

Objective Roots Test is one of the previously mentioned instruments. It would just find Rational Roots that is numbers $x$ which can be communicated as the remainder of two numbers

The Rational Root Theorem expresses that on the off chance that a polynomial zeroes for a normal number P/Q P is a component of the Trailing Constant and Q is a variable of the Leading Coefficient

For this situation, the Leading Coefficient is 1 and the Trailing Constant is - 10.

The factor(s) are:

of the Leading Coefficient : 1

of the Trailing Constant : 1 ,2 ,5 ,10

Stage 2 :

Quadratic conditions:

2.1 Solve  $x^{4} - x -10= 0$

Looking for an interval at which the above polynomial changes sign, from negative to positive or the other way around.

Technique for search: Calculate polynomial qualities for all number focuses between $x = -20$ and $x = +20$

Tracked down difference in sign between $x = -2.00$ and $x = -1.00$

Approximating a root utilizing the Bisection Method :

We presently utilize the Bisection Method to estimated one of the arrangements. The Bisection Method is an iterative strategy to inexact a root (Root is one more name for an answer of a situation).

The capability is  $F(x) = x^{4} - x - 10$

At $x = - 1.00 F(x)$  is equivalent to $- 8.00$

At x = - 2.00 F(x) is equivalent to 8.00

Naturally we feel, and evenhandedly thus, that since $F(x)$ is negative on one side of the span, and good on the opposite side then, at that point, some place inside this stretch, $F(x)$ is zero.

x = - 1.697471857

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