5) 1, -4, 0, -1

Q: . Every polynomial function of odd degree with real coefficientswill have at least___________ real…

A: Every polynomial function of odd degree with real coefficients will have at least  _____1_____  real…

Q: Find a polynomial f (x) of degree 5 that -4, -1, 3 (multiplicity 2), 0 Leave your answer in factored…

A:

Q: 10. Write a third-degree polynomial f(x) with integer coefficients and zeros of 5, -, and 4.

A: Let the polynomial is  fx=αx-15x--23x-4=αx-15x+23x-4=α5x-153x+22x-4 Coefficient will be integer if α…

Q: Write a polynomlal f(x) that satisfies the given conditions. Polynomial of lowest degree with zeros…

A: Since x=-4 is a zeros so, (x+4) is a factor of f(x) Since x=1 is a zero so, (x-1) is a factor of…

Q: Show that the Chebyshev polynomials have thefollowing properties: Tm(Tn(x)) = Tmn(x)

A:

Q: Suppose ƒ(0) = 1, ƒ'(0) = 2, and ƒ"(0) = -1. Find the quadraticapproximating polynomial for ƒ…

A:

Q: Roots of 1, 2, -4 y-in

A: Polynomial: We need to find a polynomial whose degree is even. Roots are 1,2,-4 y=intercept is -36…

Q: Write a polynomial f (x) that satisfies the given conditions. Express the polynomial with the lowest…

A:

Q: Write a general polynomial q(z) of degree n with coefficients that are bo, b,, b2, ..b,. What are…

A:

Q: Find a polynomial function of smallest degree with integer coefficients that has the given zeros.…

A:

Q: Suppose a polynomial function of degree 5 with rational coefficients has the given numbers as zeros.…

A: Given query is to find the 5th zero.

Q: A 4th degree polynomial has zeros -5, 3, i, and -i. Which could represent the function defined by…

A: here it is given that A 4th degree polynomial has zeros -5,3, i and -i

Q: Give one example of a polynomial of degree 4 that has a zero at x=5 with multiplicity 2 (there is…

A:

Q: Determine a possible 3rd degree polynomial function in factored form with its only (3, 0) and (-2,…

A:

Q: Every polynomial function of odd degree with real coefficients will have at least…

A: To determineEvery polynomial function of odd degree with real coefficients willhave atleast

Q: Form the polynomial equation with integral coefficients whose only roots are given. 3,4,2

A: if a is the root of the polynomial then (x-a) will be the factor of the polynomial  And we can write…

Q: Use the Intermediate Value Theorem to show that thefunction f1x2 = 4x3 - 2x2 - 7 has a real zero in…

A: Given: fx=4x3-2x2-7; x∈1,2 We know that for a polynomial functiony=fx in x∈a,b, if fa and fb have…

Q: Find a polynomial of the specified degree that has the gi Degree 4; zeros -2, 0, 2, 4

A:

Q: Determine the linear Lagrange interpolating polynomial that passes through the points (2, 4) and (5,…

A:

Q: Write a polynomial f (x) that satisfies the given conditions. 1 1 (multiplicity 1) and with f(0) =…

A: f(x)=ax+15x+15x-12 f(0)=a·15·15·-12 1 = -a50 a = -50

Q: Determine the third degree Newton polynomial which passes through the data points (0,1); (1, 0); (2,…

A: The objective is to determine the third degree Newton polynomial which passes through the data…

Q: Write a polynomial function of least degree with integral coefficients that has the given zeros. for…

A:

Q: Find a polynomial of least degree with only real coefficients and having the given zeros. (2+i,0)…

A: Let f(x) be the polynomial of least degree having zeros 2+i and 3.Since the complex number 2+i is a…

Q: Construct a polynomial function of least degree possible using the given informatior Real roots: -1,…

A: Given that the function has real roots at -1, 1, 3.  So the function is in the form of…

Q: Form a polynomial equation with integral coefficients whose only roots are given 1/2,square root of…

A: To find the polynomial for given roots Roots are 1/2, √2 and - √2

Q: Find the polynomial with thats has degree 3 and Zeros 2,-1 and 3

A: To find the polynomial with thats has degree 3 and Zeros 2, -1 and 3.

Q: 2. Identify the approximate input values of any relative maximums and minimums of this 5th degree…

A: I am going to solve the given problem by using some simple algebra to get the required result.

Q: Show that the polynomial z5 + 14z + 2 has four zeros in the annulus </2 < 2.

A: Given

Q: Find a polynomial function of degree 3 with the given numbers as zeros Assume that the leading…

A: Given ,degree of polynomial 3leading coefficient vs 1Zero's of functions-16,0,5

Q: 5. Write the equation in factored form of a degree 3 polynomial function with roots at -2, - 3, and…

A:

Q: Find a Polynomial with integer Coeffcients that Conditions. given Satisfies 'Ithe P has degree 3 and…

A: Given, Polynomial has degree 3 and zeros 5 and i

Q: Does there exist a polynomial of positive degree in ℤ6[x]Z6[x] that is a unit?

A: First, we understand how units in R[x] are identified. Let R[x] be an integral domain. An element…

Q: O mult. 2, -2i

A:

Q: 6) -5, 2+i

A:

Q: 2-1n 7LX1, Show that the distinct polynomial s x+x and x+X determine the Sange function From Zz bo…

A: We have to show that,  the distinct polynomials x4+x  and x2+x in ℤ3x determine the same function…

Q: th integral coefficients tha D4, 3+i

A: The integer coefficient property is stated as If the polynomial with real coefficients , has a root…

Q: Find a polynomial of least degree with only real coefficients and having the given zeros. 2 + i, 3

A: Given

Q: Write the polynomial f(x) that meets the given conditions. Degree 3 polynomial with interger…

A:

Q: Suppose​ f(x) is a 7th degree polynomial. Using a few complete​ sentences, explain why we are…

A: Given f(x) is a 7th degree polynomial.  Recall: fundamental theorem of algebra:  If f(x) is 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: Write a polynomial f (x) that meets the given conditions. 4) Polynomial of lowest degree with zeros…

A:

Q: Suppose a polynomial function of degree 5 with rational coefficients has the given numbers as zeros.…

A:

Q: 2. Find a polynomial that interpolates (-1,4) and (3,6), then find the value of f(x) at x=0 and x=…

A:

Q: Find a polynomial of the specified degree that satisfies the given conditions. Degree 4  zeros −1,…

A:

Q: 8-3 mult. 3, 0

A: Given  Zeros of a polynomial  -3 mult. 3,  0

Q: 15) 2, 3, 5, -4 16) 1, 3, -4

A: 15)  The zeros of the function are 2, 3, 5, -4

Q: 13) -1, 3, 4 14) 0, -5, -4

A: Given; 13)  -1, 3, 4 14) 0, -5, -4.

Q: Write a polynomial function of least degree with integral coefficients that has the given zeros: 1)…

A:

Q: Suppose that a polynomial function of degree 4 with rational coèfficients has -2 +51, 5-5 as zeros.…

A: Complex root :  The complex conjugate of a complex zero must also be a zero . So if you have any…