53-56 - Polynomials with Specified Zeros Find a polynomial with real coefficients of the specified degree that satisfies the given conditions. 53. Degree 3; zeros -, 2, 3; constant coefficient 12 54. Degree 4; zeros 4 (multiplicity 2) and 3i; integer coefficients; coefficient of x² is -25 55. Complex Zeros of Polynomials Does there exist a polyno- mial of degree 4 with integer coefficients that has zeros i, 2i, 3i, and 4i? If so, find it. If not, explain why. 56. Polynomial with no Real Roots Prove that the equation 3x* + 5x² + 2 = 0 has no real root.

Q: 5. Use Descarte's Rule of Signs to determine the possible number of positive and negative roots of…

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Q: Form a polynomial whose zeros and degree are given.   ​Zeros: −4​, multiplicity​ 1;    1​,…

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Q: 53-56 Polynomials with Specified Zeros Find a polynomial with real coefficients of the specified…

A: Given : 3x4+5x2+2=0 To find out the roots we solve for x First we write the given equation in…

Q: 53-56 Polynomials with Specified Zeros Find a polynomial with real coefficients of the specified…

A: To find a polynomial with real coefficients of the specified degree that satisfies the given…

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Q: a) Find a third-degree polynomial f(x) with integer coefficients and with zeros of 2 + i and . b)…

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A: Given  Remainder = -7 when divisor (x-2)  Roots are x= 3/2 and -5  To find  polynomial with expanded…

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Q: 1.a

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Q: a. Find the polynomial of degree 4 that has a zero of multiplicity 2 at x = 3, and zeros of…

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Q: 9. Find a fourth-degree polynomial with integer coefficients that has zeros 3i and –1, with -1 a…

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Q: The Fundamental Theorem of Algebra states that any polynomial equation of degree n must have exactly…

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Q: The polynomial P1x2  5x21x  4231x  72 has degree. It has zeros 0, 4, and . The zero 0…

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Q: 53-56 Polynomials with Specified Zeros Find a polynomial with real coefficients of the specified…

A: We have to construct an equation with degree 3, zeroes -12,2,3 alongwith constant coefficient as…

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Q: 37–46 ■ Finding a Polynomial with Specified Zeros Find apolynomial with integer coefficients that…

A: Finding a Polynomial with Specified Zeros Find a polynomial with integer coefficients that…

Q: 1. Given an expression for f(x) of degree 3 with roots x = -7 and x = -6, where the root at x = -6…

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Q: Form a polynomial​ f(x) with real coefficients having the given degree and zeros.   Degree​ 4; ​…

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Q: 2. Find a polynomial of degree 5 whose zeros are -4, 2, 0 (multiplicity 3) and contains the point…

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A: Solution:- according to terms and condition i have solved question1 for next question please repost

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Q: 1. Find a polynomial of degree 6 with real coefficients and having zerós -3, 0, 2, 5, and 1+2i.…

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Q: 3. True or False a. A polynomial of degree 5 has 6 real and imaginary zeros. b. The opening of an…

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Polynomials

Try substituting 1. You will get 6 and not 0. Try other real values also. What About -2? Let us check.