Write down the statement for the remainder theorem for a CUBIC Equation. Once completed verify this statement by performing long division and checking that the rer is 5 for the following; 11. x' +3x-13x-10 X-3

Q: An nth degree polynomial will have at most n+1 real roots. O True O False

A: No, that is not possible. The only reason that an n-degree polynomial has max n roots is that it can…

Q: Use the Remainder Theorem and synthetic division to find each function value. Verify your answers…

A: Note:- according to the company policy we can attempt only three subpart of a question so please…

Q: If x4 −2x3 −12x2 +10x+ 3 = 0 has the roots 1 and −3,

A:

Q: When dividing x^3+2x+4 by 3x+2 in Z11[x], the remainder is

A: 1)  The statement is true  Now to see  ho the given polynomial is irreducible or not

Q: Find all the real roots of the following polynomial equation. 1.) (3x+2)(x2-25)=0 2.)…

A: As per bartleby guidelines we only give first question answers.

Q: Find the roots of the polynomial: f(x) = 3xª+5x³+20x² +30x+12.

A: fx=3x4+5x3+20x2+30x+12

Q: Find an integer coefficient cubic that has x = 1 and x = 2+ /3 as zeros.

A: Given: The two zeros of a cubic polynomial are x=1 and x=2+3.

Q: 4. The polynomial equation whose roots are {-1, - ½ and 3} is А. 2х3- Зx2 - 8х-3%3D0 В. х3 - 6х2 - х…

A:

Q: Show that the equation x4 + 4x + c = 0 has at most two real roots

A:

Q: Find a polynomial f(x) of degree 4 that has the following zeros. 1,-7,0,2 Leave your answer in…

A: The objective is to find the polynomial of degree 4. If a is the zero of any polynomial f(x), then…

Q: find a real root of the equation x + x + x + 7 = 0 by using Bisection method

A:

Q: Approximate the roots of the polynomial f(x) = X3 - 7X + 6 using Bolzano method

A:

Q: Approximate the roots of the polynomial f(x) = X3 - 7X + 6 using Bolzano method.

A:

Q: 2) x- 7メ r Sx3 +93 ×2 イ2x-72=0 R) x5-2x4 -15x°t 10×*+イX-18=0

A:

Q: Solve for the root using Bisection, Newton Raphson, and Secant Method 1. 3x³4x²-3x - 2 = 0

A: Given that 3x3-4x2-3x-2=0 Let fx=3x3-4x2-3x-2, then f0=-2, f1=3-4-3-2=-6,…

Q: Solve for all the roots of x using Bairstow’s Method starting at r1 = 0.25 and s1 = 8.75 of the…

A: Solution:-

Q: Every polynomial equation of the nth degree has n real roots Select one: O True O False

A: Given :   Every polynomial of degree of nth degree has two types of roots : Real and Non-real /…

Q: Find the roots of the functionf(x) = (2x−1)·(x2+ 2x−3) withx∈R

A:

Q: For any n > 1, prove that the product of the nth roots of unity is(-1)n+1.

A:

Q: show that the equation 3x+2cosx+5=0 has exaclty one real root.

A: f(x)=3x+ 2 cos x +5

Q: A. by extracting square roots. 1 x2 = 169 2.9b2 = 25 3. (3y- 1)2 = 0

A: Multiple questions-"As per our guidelines we are suppose to answer only one question.Kindly re-post…

Q: 11. If f(x) = -3x2 - 4x + 1, use synthetic division to evaluate f(4)

A: You have asked multiple unrelated questions in the same post. I have addressed the first one. Please…

Q: The equation y = 4r + 20z2 19z + 30 has one root at x = -6. Use synthetic division to find a…

A: Given:  The equation is y=4x3+20x2-19x+30   One root x=-6  Using synthetic division method the…

Q: Find real root of the equation x^3-3x-5=0 by the bisection method

A: According to the given information, it is required to find the real root of the given equation using…

Q: Suppose the coefficients of the cubic polynomial p(x) = a +bx+cx^2+dx^3 satisfy the equation:…

A:

Q: Given the polynomial: f (x) = 2x° + mx* – 40x° + nx² + 218x – 168 And that two of the roots are x= 1…

A:

Q: Find a polynomial of degree 4 that has a real coefficient and has 3,2 and 2+i as some of its roots

A:

Q: Show the work steps for finding the roots of x- 13x+36 algebraically.

A:

Q: The equation that gives the depth x to which the ball is submerged under water is given by x²…

A: Given equation is x3 -0.165 x2 +3.993×10-4 =0 Take  fx = x3 -0.165 x2 +3.993×10-4  Let initial…

Q: The remainder upon the division of x75 + 6 by x – 3 in z, is: 1

A:

Q: b) Write down the polynomial equation for (1,-2) and (4,3) using Lagrange Method.

A: Let x,y =1,-2 and x2,y2 =4,3Then by Lagrange 's method , interpolating polynimial is given…

Q: Express as a polynomial.

A: .

Q: 2)(x°tx -35)(x2 -ext 1a) Lxス+axー27) =D0 2) Cax2 +SX -う)(3x<+5X-2) [xミ qxt 10) =0 3) Casx2-1) (xメ-…

A:

Q: 4) -3, -4, 5 ansurer -2 -3 3 answer 6) - answer .

A:

Q: Express the quadratic form Q(x1, x2,x3) = 6x3 +3x3 +3x3 – 4x1.x2 – 2x2x3+4x3x1 to the sum of square,…

A: We need to use eigen values and eigen vectors of co efficient matrix

Q: f(x) = -5x6 + 8X5 + 9X4 -10X3 +2X2 -22X +45

A: To do the calculations in Excel, first enter the numbers in separate cells. Each number is…

Q: Determine the root of the given equation f(x) = x³ + 2x2 – x- 2 = 0 for x %3D %3D using bisection…

A: Using Bisection method

Q: The remainder upon the division of x + 4 by x – 4 in Z, is: 1. None

A:

Q: 2.) × 1+2xー13x2- 14xt2イ=0

A: To find  The complete set of possible rational roots.

Q: 3. If x=-2 is one of the roots of 6x'+11x - 4x -4 = 0, find the other two roots of the polynomial…

A:

Q: In Unit 1 you have learnt about the remainder theorem and long division. Compare and contrast the…

A: Hello. Since your question has multiple sub-parts, we will solve first three sub-parts for you. If…

Q: 4. Find the roots of the following over C (a) x2 + 18x + 97 (b) x3 +3x2 - 6x -8 yes that is a cubic…

A: a)  x2+18x+97 Using the formula, x=-b±b2-4ac2a x=-18±324-3882x=-18±-642x=-18±i82x=-9±4i   c)…

Q: Prove, algebraically, that the following equations are polynomial identities. Show all of your work…

A: The solution are next step..

Q: find the four zeroes of the polynomial z^4+4, one of them being z0=2^1/2e^ipi/4=1+i.then use those…

A:

Q: x to the third minus 512 over x-8 and must be solved using synthetic division.

A: First of all, consider the dividend and the divisor.

Q: Find the exact roots 1/4x² + 3/2 x³ + 1/2x²-9/2x-15/4-0

A:

Q: Calculate the roots of the following polynomial equations: (a) x – 6x2 + 1lx – 6 = 0 given x = 1 is…

A:

Q: Find x so that the distance between (−4, 5) and (x, 3) is  the square root of 29

A:

Q: Find the number in {x E R:-2<x<2} such that the sum of that number and its square is a maximum.…

A: