Express f (x) = x + 3x - x2 + 5x – 2 in terms of Legendre polynomials.

Q: Show that the polynomial function f(x) = x3 - 2x - 5 has a real zero between 2 and 3.

A: since f(x) is a polynomial function so it is continuous at every point.

Q: What type of polynomial satisfies f"(x)=0 for all x?

A: Topic-polynomial

Q: The fourth-degree polynomial f (x) = 230x* + 18x³ + 9x² – 221x - 9 has two real zeros, one in [-1,…

A: Bisection method: This method is also called the interval halving method and it is used to find the…

Q: Express f(x)= 4+ 6 x² + 7 x + 2 in terms of Legendre Polynomials.

A:

Q: 1. Express the polynomial f(x) = 4x3 – 5x2 + 2x – 3 as a power of x + 2.

A:

Q: Consider the polynomial function 1 f(x) = 6x° + 10æª 12 24x %3D -- - - 19

A: The given polynomial,f(x)=6x9+10x4-x312-24x-119

Q: Which type of polynomial satisfies f 111(x) = 0 for all x?

A: To find: The polynomials that satisfy f'''(x)=0

Q: Express the polynomial x3 + 2x+3 EZ-[x]as a product of irreducible polynomials of 75[x].

A:

Q: Find the remainder when f(x) = x7 + 3x5 + x - 1 is divided by x2 +1 in Z5[x].

A:

Q: Show that f(x)=4x^5+x^3+7x−2  has exactly one real root.

A: Given, f(x)=4x5+x3+7x-2

Q: Use the Intermediate Value Theorem to show that the polynomial f(x) = 4x* - 7x2 + 2 has a real zero…

A: topic - intermediate value theorem

Q: Find Ao, A1, and Az in rewriting the function of f(x=2vx 0マx in terms of Lagure polynomial ョーの

A: Given: Let us consider the given function  fx=2x       x≥00             x<0 and the Lagure…

Q: product of irreducible polynomials.

A:

Q: Prove that f (x) = x3 + 3x2 + 6x has precisely one real root.

A: Number of real zeros of a quadratic equation can be determined using its discriminant. For a…

Q: 8 (x)= 1 centered at a =0 1+x

A:

Q: find the 3rd degree maclaurin polynomial of f(x)= (x-2)/(x+3)

A:

Q: What is a polynomial in x?

A: The x happening in a polynomial is generally referred to as a variable or an indeterminate. When the…

Q: 4 Use the Intermediate Value Theorem to show that the polynomial f(x) = 3x* - 10x +4 has a real zero…

A: Given interval is -1 to 0 Use intermediate value theorem to show that polynomial has a real zero…

Q: 6. Use the Remainder Theorem to evaluate f(x) = 10x* - x3 + 13x2 – 9x + 17 at x =-.

A: Since the student has mentioned to solve question number (6), so we are solving only question number…

Q: .5) a) Express the polynomial f(x) in terms of Legendre polynomials where f(x) = 1-3x + 3x2

A: Given ,            f(x) = 1-3x+3x²

Q: express f(x) =x³+2x²-x-3 , in term of lagendre polynomial

A: To express the given function f(x)=x3 +2x2 -x-3 in terms of Lagendre polynomial.

Q: The equation that does not represent a polynomial function is Oy = - = -x + Oy = x 10 - x + √22 + x…

A:

Q: Determine the real root F (x)=26+85x-91x^2+44x^3-8x^4+x^5 Graphically

A: . The real roots of an equation are the x-intercepts of the graph.

Q: Find a polynomial f (x) that satisfies the equationxf"(x) + f (x) = x2.

A: Quadratic equation are those equation in which highest power of the equation is 2 and it has two…

Q: Express the polynomial x3+2x+3 in Z5[x] as a product of irreducible polynomials of Z5[x] .

A: Explanation of the answer is as follows

Q: show that the polynomial f(x)= x^3-2x -5 has a real zero between 2 and 3

A:

Q: Which polynomial function in standard form has a root of multiplicity 1 at x= 3, and a root of…

A: A polynomial function has a root of multiplicity 1 at x=3, and a root of multiplicity 2 at x=4

Q: Find sum of two polynomial f(x) = x^3-7x+6 and g(x) = 5x^3-8x+1

A:

Q: Express the polynomial f(x) = 2x² + 3x³x²+x-2 in the form f(x)=b₁(x - 5)¹. i=0

A:

Q: f (x) = x,³x2² + x1³x3? + x,?x,³ + x,²x3³ + x2³x3² + x2³x3?

A: The given polynomial is not symmetry hence it can not be written in elementary symmetry polynomial

Q: Use the Intermediate Value Theorem to show that the polynomial function f(x) = x3 + 2x − 1 has a…

A: f(x)=x3+2x-1, [0,1]

Q: Let f(x) = 2x² + 8x – 9. According to the definition, -

A: Derivative: - Differentiation is the pace at which one quantity changes in relation to another. The…

Q: If x^3=3x^2, then what is x using the Zero-Product rule?

A: Given that x3 = 3x2.

Q: Express as a polynomial.

A: .

Q: list the potential rational zeroes for this polynomial function f(x)= 3x^5 - x^2 + 2x + 24

A:

Q: Which type of polynomial satisfies f ,,, (x) = 0 for all x?

A: Let f(x) be a polynomial such that f'''(x)=0 for all x Integrating both sides ,we get Again…

Q: Use the Intermediate Value Theorem to show that the polynomial function has a zero in the given…

A: Intermediate value theorem: - The intermediate value theorem asserts that if "f" is a continuous…

Q: Express the polynomial f(x)=3-12x + 21x² 16x³ + 5x4 4 f(x) = Σbi(r - 1). i=0 in the form

A:

Q: Express the second order polynomial p(x) = x^2 + 4x + 13 in the sum of square form

A:

Q: The polynomial f(x)=(x−2)^3=(x−2)(x−2)(x−2) has x=2 as a zero four times. true or false?

A:

Q: Plot the zeros of each polynomial on a line together with the zeros of its first derivative. i) y =…

A:

Q: pind the Maclaurin polynomial of degree 3 for the function f(x)=è=7x

A: Given function f(x)=e-7x. The objective is to find the Maclaurin polynomial of degree 3.

Q: Show that f(x) = 2x3 + 3x2 − 36x is not one-to-one on (−∞, ∞).

A: Given: f(x)=2x3+3x2-36x, -∞,∞

Q: - -2x4 + x - 2x² + 3x – 1.

A:

Q: 8. Find the zero of f(x) = 5x - 3. %3D

A: Since you have posted more than one question, we solve the first one for you. For the remaining…

Q: Express f(x) = 4x3 + 6x2 + 7x + 2 in term of Legendre Polynomials.

A: The Legendre equation is, 1-x2d2ydx2-2x dydx+nn+1y=0 The polynomial denoted by Pnx is called the…

Q: xỉ + x + x – X1X2X3

A:

Q: Express f(v) 4 + 6 x² + Z x + 2 in terms of Legendre Polynomials.

A:

Q: Show that the polynomial function f(x) = 3x3 - 10x + 9 has a real zero between -3 and -2.

A: Given that, fx=3x3-10x+9

Q: Does f(x) = x3 - x - 5 have a real zero between 1 and 2?

A: Intermediate value theorem: Let f be a polynomial function. If f(a) and f(b) have opposite sign then…