Let a polynomial y = a0 + a1x + a2x 2 + a3x 3 + a4x 4 be given with a0, a1, a2, a3 and a4 are constants to be determined. If the polynomial passes through the points (−2, 5),(−1, 2), (−3, 6), (1, 3) and (2, 7), find the exact values of all the coefficients of the polynomial.

Q: Find the real zeros of the polynomial function. f(x) = 4x³ - 5x² − 7x + 2 O-1, 2, 4 01, -2, -4 01,…

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Q: 4. In each part, determine whether the polynomial is a linear combination of P, = 2+x+x², P, = 1-x²,…

A: We have to determine whether the polynomial is a linear combination of given polynomials.

Q: find a polynomial function with real coefficients that has the given zeros.  A) 0,2,3i B) 1,1,2+√3…

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Q: 13. Find the equation of the third degree polynomial containing the points (1, -7), (0, 4),(3, -2)…

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Q: Find all zeros of the polynomial function. Ax) = x* - 2x + 8x2- 32x – 128 O -4, -4, -2, and 4 O -4,…

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Q: Find the zeros of the polynomial f (x) = x³ – x2 + 4x – 4 О 1,2, -2 O -1, 2, -2 О 1,21, -2i O -1,…

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Q: The cubic polynomial shown below has zeroes only at x= -3 and x = 5 and passes through the point (2,…

A: To find y value

Q: 19. Which polynomial function has zeros 1, 1+i, and 1-1? A P(x)=x³ -x² +2x + 1 B P(x) =x -4x² + 3x –…

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Q: Suppose we want to find the unique second degree polynomial functionp(x) such thatp(−2) =−1,p(2)…

A: Given :p(-2) =-1p(2) = -1p(3) = -6General form of polynomial is p(x) = Ax2 + Bx + CTherefore;p(-2)…

Q: Find a polynomial function that has the given zeros.−2, −1, 0, 1, 2

A: To Find a polynomial function that has the given zeros Given that the zeros are −2, −1, 0, 1, 2.

Q: Graph the polynomial P(x) = -(x + 3)3 + 8, showing clearly all x- and y-intercepts. y y 20 50- 10 40…

A: x - intercept , where the graph cut the x - axis . And y - intercept , where the graph cut the y -…

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

A: Sum of zeros = -(b/a)  product of zeros = (c/a)

Q: Rewrite the polynomial in the form ax + by + c and then identily the values and c. x - 1- 2y

A: To identify the value of a,b,c

Q: If alpha and beta are zeroes of x^-x-30,then form a quadratic polynomial whose zeroes are –2alpha…

A: α & β are zeroes of x2-x-30. That is, α+β=--11  &  αβ=-301   ∵If α & β are zeroes of…

Q: The zeros of the polynomial P(x) = x* + 3x2 - 4 are %3D (a) 2i,-2i, i and - i (b) 2,-2, i and – i…

A: To find the zeroes

Q: 1. Find the zero's (aka roots) of the polynomial function and state the multiplicity of eac (i) (2.x…

A: Put polynomial =0

Q: Find all the zeros of the function and write the polynomial as a product of linear factors. х4 +…

A: Lets find the zeroes:           x4+13x2+36=0…

Q: A polynomial has only zeroes 1, 2, and 5 with the multiplicities 4, 2 and 1 respectively. What is…

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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: C. Pick the correct roots/zeros in the following polynomial equations: 1. x-7x+ 6 0 (6, -1, 2 1,…

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Q: , (-1, 13), and (2, -2).

A: To find the value of a, b and c in the polynomial ax2+bx+c passes through the point (1,1) , (-1,13)…

Q: 7. Find an equation of a polynomial that has x-intercepts of 2, - 6, and 1 and it passes through a…

A: Points where polynomial cuts x axis are the factors of polynomial with some constant  we can write…

Q: If a and B are the zeroes of the polynomials f (x) = x² – 5x +k such that a -B =1 find the value of…

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Q: 42. If the coefficients of a polynomial function are all positive,then the polynomial has no…

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

A: Given: Zeros of Polynomial:13, 4-i, 4+i To Find: Polynomial of smallest degree with integer…

Q: Find a polynomial f (x) of degree 5 that has the following zeros. -7, 8, 6, -2, 4 Leave your answer…

A: As, f(x) has five zeros and they are -7, 8, 6, -2, 4, then f be of five degree polynomial.Therefore…

Q: Obtain a 2nd degree polynomial representing the following points. 2 3 20 40 -40 -20

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Q: How do I  find the polynomial function with the given zeros: i, -i, √ 3, -√ 3

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Q: Let P0. (x) denote the quadratic polynomial that interpolates the data {(xo, yo), (x1, y1), (x2,…

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Q: Form the polynomial function that has the following real ZEROS: 3,-1, 2, 4 Section 3.1 O z4 + 2z3 -…

A: Given point is; x = -3,-1,2,4   1) x4+2x3-14x2-13x+24  we find the factor of this function and then…

Q: 1.  Give a polynomial function that only has x intercepts of 2, 4, and -1 with a y intercept of -8.

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Q: Find a polynomial of degree 3 (here ao, a1, a2, a3 are real numbers) such that p(x) = ao + a₁x +…

A: This question can be solved using the concept of solving system of linear equation using matrix.

Q: Let P(x) be a polynomial of degree 5 with roots 2, – 5 and (3 + i). Write P(x) as a product of…

A: It is given that the roots of 5 degree polynomial are 2,-5,3+i

Q: If a,ß the zeroes of the polynomial 2y + 7y + 5, Find the value of a+ß+aß

A: For finding zeroes I used factor method for quadratic equation I completely solved in the 2nd step…

Q: Find the polynomial of degree 3 with leading coefficient -2 and zeros at 2, 4, and -3. a) O-2- 10²…

A: The polynomial will bekx-αx-βx-γwhere 'k' is leading coefficient α,β,γ are zerossubstitute…

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

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Q: If a, Band y are the zeroes of the polynomial p (x) = ax'+ 3bx² + 3cx+ d and having relation 2B =…

A: Option (c) is correct.

Q: 2. Determine whether the polynomial 1+ x + ? is a linear combination of P, = 2+x+x², p, = 1-x, p, =…

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Q: Find a polynomial f(x) of degree 5 that has the following zeros. 6, -9, 4, 0, 3. Leave answer in…

A: topic - polynomials

Q: Which polynomial function has zeros -2, ½, 2, 1? O A. y = 2x^4 - 3x^3 – 7x*2 +12x - 4 O B. y = 2x^3…

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Q: 3. Find both linear and quadratic interpolating polynomials for the points (-2,-13) , (-1,-3) ,…

A: We take given pairs of points as (x, y) x y -2 -13 -1 -3 1 -1 2 -9 3 17 We have…

Q: Form the polynomial function that has the following real ZEROS: -1, 1, 0, –3 Section 3.1 O a+3a + a²…

A: See attached file for a step by step explanation to find the required polynomial.

Q: Find values of a, b, and c such that the graph of the polynomial p(x) = ax²+bx+c passes through the…

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Q: Find a polynomial of degree 5, and zeros of-4,-2, 0, 2, and 4 O a. x- 20x + 64x | O b. x+20x+64x…

A: Given for a polynomial f(x) of degree 5 , roots are -4, -2, 0, 2 & 4

Q: Find the polynomial f(x) of lowest degree with only real coefficients and having the zeros 3+ V2, 3-…

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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: Show that the given values for a and b are lower and upper bounds for the real zeros of the…

A: Solution:- Any given value is said to be upper bound for the zeros of the polynomial if all the…

Q: 6. Give an example of a polynomial function that has each of the following end behaviours: a) As…

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Q: Show that the given values for a and b are lower and upper bounds for the real zeros of the…

A: Solution:-

Q: Find the function in stardard form of the polynomial that has the roots x=1,2 and -5. (Assume that…

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