Determine the maximum number of real roots and possible real roots of the following polynomial equations: Polynomial Equation 1. x4-81 =0 2. x3-2x2-5x+6= 0 3. x3-6x2+11x-6= 0

Q: If a + bi is a root of a polynomial equation with real coefficients, b + 0, then. equation. is also…

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Q: Find a polynomial function with real coefficients that has the given zeros.2, 2, 1 + i

A: Given- The roots are 2,2 and 1+i. To Find- The polynomial function.

Q: Find the roots of the quadratic polynomials: f (x) = x2 − 2x − 1

A: We know that, for an standard equation fx=ax2+bx+c, roots are calculated by using quadratic formula…

Q: Find the polynomial equation whose zeros are 2 of multiplicity 2, 1 and -2

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Q: Find the roots of the quadratic polynomials: f (x) = 4x2 − 3x − 1

A: Given f (x) = 4x2 − 3x − 1

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

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Q: must every polynomial equation with real coefficients of degree 3 have at least one real root? Why

A: Recall: Fundamental theorem of Algebra: Any polynomial of degree n with real coefficient has n…

Q: Find a polynomial function f of degree 4 whose coefficients are real numbers that has the zeros…

A: Given: Zeros of polynomials are 1,1,and -4+i.

Q: Find the polynomial function of lowest degree with rational coefficients that has the given numbers…

A: Given zeros

Q: Find all real solutions of the polynomial equation x* - 7x + 42x - 36 = 0. х%3D 1,-36, 12 х%3D 1,-7,…

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Q: Find the equation of the polynomial with roots (–√3, 0) and (7i, 0), real coefficients, and passing…

A: Step I :   Given :   Roots : -3 , 0 & 7i , 0and passing through the point 1 , 200Find the…

Q: Write the equation of a third degree polynomial in standard form (multiply out) with the given…

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Q: solve the polynomial for all roots: f(x)=x3-4x2-5x+20

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Q: 5. Find a polynomial equation with real coefficients that has the given zeros: - 3, 4i

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Q: How does the linear factorization of f(x), that is, AX)=an (x-c1)(x-c2) (x-C). show that a…

A: Here the linear factorization of the function f(x) is given as:…

Q: Find an equation of a degree 3 polynomial (in factored form) with the given zeros of f(x): 3,3,-1 .…

A: see 2nd step.

Q: Find a possible formula for a polynomial with degree n=2 and the zeros are x = -4 and x = 11.

A: Let the polynomial at 2nd degree be             P(x) = x2 + ax + b Given, Zeroes are x = -4 and x…

Q: Find an equation of the cubic polynomial f(x) = ax3 + bx2 + cx + d that passes through the given…

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Q: In Problem,explain why the facts given are contradictory.

A: Zero of a function is a point in its domain for which the function takes the value equal to 0. A…

Q: Show that if the quadratic polynomial f (x) = x2 + rx + s takes on both positive and negative…

A: Find the real roots of the polynomial,

Q: Write the equation of a third degree polynomial in standard form (multiply out) with the given…

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Q: Find a polynomial of degree four that has zeros -3, 0, 1, and 5, and the coefficient of x3 is -6.

A: We need to find a polynomial of degree four that has zeros -3, 0, 1, and 5, and the coefficient of…

Q: Find the zeros of the quadratic polynomial f(x) =abx2+(b2-ac) x-bc,and verify the relationship…

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Q: Find the roots of the quadratic polynomials:(a) f (x) = 4x 2 - 3x - 1 (b) f (x) = x 2 - 2x - 1

A: We set them equal to 0 and solve for x we first factor the left side then we set each factor equal…

Q: 9.)-2, 5 -3.2 3

A: Since you have posted a multiple question according to guildlines I will solve first question (i.e…

Q: find a polynomial function of lowest degree with rational coefficients that has the given numbers as…

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Q: Find a polynomial f (x) of degree 3 that has the indicated zeros and satisfies the given condition.

A: Given: A 3 degree polynomial with zeros -3,-2,0.

Q: Give a polynomial equation with integral coefficients that has the following roots. 0, -3, -1, 2

A: This question is related to polynomials, we will solve it using given information.

Q: Find an 4th degree polynomial function with real coefficients whose zeros are 4,–1,2, v2i and a…

A: Here degree of polynomial is 4 so it has 4 roots.

Q: find a degree 3 polynomial having zeros 3,-7, and 4 and leading coefficient equal to 1.

A: Given: A degree 3 polynomial having zeros 3, -7 and 4 and leading coefficient equal to 1.

Q: Find the zeros of the quadratic polynomial f(x) =abx2+(b2-ac) x-bc, and verify the relationship…

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Q: DETERMINE THE ROOTS OF THE EQUATION USING: REGULA FALSI METHOD f (x) = x³ – 3x + 1 Using a…

A: Roots of the equation

Q: Create a polynomial equation with real coefficients that has 2 and 1-i as roots.

A: To create a polynomial equation with real coefficients that has 2 and 1-i as roots.

Q: Find a polynomial f (x) of degree 3 that has the following zeros. 0, -2, 1 Leave your answer in…

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Q: find a polynomial function with real coefficients that has the given zeros 0, 3, 2i 4, 1+√3 i

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Q: Find a quadratic polynomial whose zeroes are (i)3, -4 (i)2, 1

A: Quadratic  equation = x2-(Sum of zeroes)x + product of zeroes =0

Q: Find a degree 3 polynomial having zeros -1, 2 and 5 and the coefficient of x^3 equal 1. The…

A: Here we find the polynomial whose zeros are given.

Q: Find the zeroes of the polynomial f(u) =4u2+8u,and verify the relationship between the zeroes and…

A: Solution: The objective is to find the zeroes of the given polynomial

Q: Determine the multiplicity of 1 as a root of a polynomial f(x) = x³ 3x¹ +4x³ − 4x² + 3x − 1

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Q: If a + bi is a root of a polynomial equation with real coefficients, b ≠ 0, then________ is also a…

A: Given: if a+bi is the root of a polynomial equation with real coefficients,b≠0, then ..............…

Q: DETERMINE THE ROOTS OF THE EQUATION USING: REGULA FALSI METHOD f(x) = x³ – 3x + 1 Using a…

A: The equation in form f(x)=0 is called a transcendental equation. If the function is continuous on…

Q: Find a degree 3 polynomial having zeros -5, 2 and 6 and the coefficient of x° equal 1. The…

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Q: Find a polynomial of degree 4 with integer coefficients that has -2 as its only real zero and (1/3)i…

A: A polynomial of degree 4 with integer coefficients that has -2 as its only real zero. Which implies…

Q: Find the zeros of the quadratic polynomial f(x) =abx2 +(b2 -ac) x-bc, and verify the relationship…

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Q: find all roots of the polynomial f(x)=(3x-2)(3x^2-5)(x^2+9)

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Q: 2. Determine the exact real roots for the polynomial equations. a) 8x¹ + x = 0 b) x³ = 5x - 4

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Q: Find an equation with real coefficients for the polynomial that passes through the point (0,…

A: we have to find an equation with real coefficients for the polynomial that passes through the point…

Q: What is the degree of a polynomial equation? What are polynomial equations of degree 1 and degree 2,…

A: given , to define degree of polynomial equation and what are polynomial equations of degree 1 and 2