Answer:
Guide for how to get your answer and your answer
step 1
Find roots (zeroes) of : F(x) = x3-9x-7
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 -7.
step 2
The factor(s) are:
of the Leading Coefficient : 1
of the Trailing Constant : 1 ,7
Lets test
P Q P/Q F(P/Q) Divisor
-1 1 -1.00 1.00
-7 1 -7.00 -287.00
1 1 1.00 -15.00
7 1 7.00 273.00
found no rational roots.
(end equation of part 2) x3 - 9x - 7 = 0
step 4
Solve x3-9x-7 = 0
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) = x3 - 9x - 7
At x= -3.00 F(x) is equal to -7.00
At x= -2.00 F(x) is equal to 3.00
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 intervl, F(x) is zero,
(1) Find a point "Left" where F(Left) < 0
(2) Find a point 'Right' where F(Right) > 0
(3) Compute 'Middle' the middle point of the interval [Left,Right]
(4) Calculate Value = F(Middle)
(5) If Value is close enough to zero goto Step (7)
Else :
If Value < 0 then : Left <- Middle
If Value > 0 then : Right <- Middle
Next Middle will get us close enough to zero:
F( -0.844759464 ) is -0.000000848
The desired approximation of the solution is:
x ≓ -0.844759464
0.844759464 is your answer..
Explanation: