Consider the polynomial function fx x5 11x4 21x3 10x2 21

Consider the polynomial function: f(x) = x^5 + 11x^4 - 21x^3 - 10x^2 -21x - 5 Objective is to find the approximation to within 10^-5 to all zeros using Newtonas method. Find the interval [a_1, b_1] in which the required real zero lies by using Maple Technology shown below. f = x^5 + 11 middot x^4 - 21 middot x^3 - 10 middot x^2 - 21 x - 5 f: = x^5 11x^4 - 21x^3 - 10x^2 - 21x - 5 al:=convert(f|_x = 2, float, 8) > al:= -47 bl:= convert (f|_x = 3, float, 8) > bl:= 409 Thus, the required interval is [a_1, b_1] = [2, 3].

Solution

we are calculating value of the polynomial at x= 2 and x= 3 and the values are coming out to be -47 and 409 of the polynomial.

Here by just looking over the change in value of the polynomial -47 to 409. We can easily judge that by the time we very our value of x between interval 2 to 3, our value of polynomial will change form -47 to 409 and in between somewhere it will be zero too.

That is what we need to find that in which interval of x, value of polynomial will be zero and our answer is [2,3]