The values of various roots can be approximated using Newton's method. For example, to approximate the value of √/10, let x =√10 and cube both sides of the equation to obtain x³ = 10, or x³ - 10 = 0. Therefore, 10 is a root of p(x)=x³ - 10, which can be approximated by applying Newton's method. Approximate the following value of r by first finding a polynomial with integer coefficients that has a root r. Use an appropriate value of x, and stop calculating approximations when two successive approximations agree to five digits to the right of the decimal point after rounding. r=(-12)3 (Type an integer or decimal rounded to five decimal places as needed.) 12

Q: d. By experiment, guess or derivation, find real numbers r and s so that An+2 + ran+1+ san = 0,…

A: Given, an+2+ran+1+san=0 as x2+rx+s=0r=-6 and s=10∴x2-6x+10=0To find relation between 3 + i and…

Q: 4. If x=-4 and x=1 are the roots of x* + 3x' - 3x +3x – 4 = 0, find the other two roots of the…

A:

Q: 1. Show that if P₁(z) is a polynomial of degree n with real coefficients and zo is root of is root…

A: Detailed solution attached in step 2.

Q: I dont know what algberic moves to solve for the inverse of a polynomial function. f(x)=192t-16t^2…

A:

Q: 3. y = 2x + 9x² + 7x - 6 Determine the first factor by utilizing the fact if substituting x = c, (c…

A:

Q: Sketch a higher degree polynomial with the following roots: -2, 3, -3, 6. f(x) 9,

A: It is given that the roots are -2, 3, -3 and 6. That is, x+2=0, x-3=0, x+3=0 and x-6=0. The…

Q: Use Newton's method to calculate the real roots of the following polynomi- als as accurately as…

A:

Q: 4. Find ALL additional real zeros of the given polynomial equation given that x = 6 is a zero of the…

A: Factors  Reals roots are x=1,-1,6,2.5,-2.5

Q: A quadratic polynomial y = 4x² + 7x − 3 has roots p and q. A new quadratic with roots r = is given…

A: