For the given polynomial o find the maximum possible umbers of the positive and the negative roots o find all the integer roots o find the non-integer real roots o find the complex roots a(x)=2x+5x++11x-49x-31x -26

Q: ertAim: To find a polynomial formula that satisfies givenigonditions. For each problem, find the…

A: First one answer

Q: The polynomial of degree 5, P(x) has leading coefficient 1, has roots of multiplicity 2 at r = 5 and…

A: Given the polynomial of degree 5 , px has leading coefficient 1 , hasa root of multiplicity 2 at…

Q: Find a polynomial f (x) of degree 3 with real coefficients and the following zeros. 4, 3+i 6. s(x) =…

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Q: Find a polynomial f(x) of degree 3 with real coefficients and the following zeros. 1, 4i s() - 0 %3D

A: We are asked to find a polynomial f(x) of degree 3 with real coefficients and the following zeroes…

Q: Find a degree 3 polynomial with real coefficients having zeros 2 and 2−2i and a lead coefficient of…

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Q: 6. Find all the roots of the following polynomials: a) p(r) = * - 3.r" +?+ 7x – 30 and b) p (r) = r*…

A: Note: Since we are allowed to solve one question at a time, we have solved the first one. Kindly…

Q: The number of zeros of the polynomial x² + 4x +1 in z 1 O None 2 4

A:

Q: For #5

A: to obtain the expression for the polynomial (satisfying the given condiitons) in the required form

Q: ind the roots of the polynomial: f(x) = x^4 + 4x^2 – 32

A: Explanation: Given that,  f(x)=x4+4x2-32     Let us suppose  x2=u Function becomes  u2+4u-32

Q: n=3 -2and 6+5i are zeros f(-1)=74 Find an nth degree polynomial with real coefficients satisfying…

A: Given zeros of the polynomial, -2 and 6+5i And n = 3

Q: Find a degree 3 polynomial with real coefficients having zeros 5 and 4i and a lead coefficient of 1.…

A: Here I am attaching image so that you understand each and every step.

Q: -10 5. Given the polynomial: 2x³ + 19x² + 32x - 21 A) List all of the possible rational roots: B)…

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Q: 5. Use long division to do this problem. Specify the quotient and remainder (10x -x- 15) (2x – 3)…

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Q: Find all the roots of this polynomial: y = x+ 6x - 5x2 +250 using Desmos and synthetic division.…

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Q: 3(x-8)(x+1)4(x-3)(x+7) for each polynomial find the all the roots and give the multiplicity of…

A: For (x-a)m, root x=a, multiplicity m

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

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Q: The polynomial of degree 5, P(r) has leading coefficient 1, has roots of multiplicity 2 at z = 4 and…

A: P(x) has a root of multiplicity 2 at x = 4 So, (x-4)² is a factor of P(x) Similarly, P(x) has a root…

Q: 1) The polynomial P(x) = x²+4x³+x²-6x+2 has roots; a, 6, 7, 8. Given the condition that aß = -1: (i)…

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Q: The polynomial of degree 5, P(x) has leading coefficient 1, has roots of multiplicity 2 at x = 2 and…

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Q: Find a degree 3 polynomial with real coefficients having zeros 5 and 4i and a lead coefficient of 1.…

A: Given Zeros = 5 , 4i⇒-4i is also the zeros of the polynomialLeading coefficient =1

Q: Find an​ nth-degree polynomial function with real coefficients satisfying the given conditions.…

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Q: nd a polynomial P(r) with rational coefficients that has the degree 5 and zeros -2, 1 + 2i and -1…

A: Complex zeros always occur in pairs Means if a+ib is one zero then  a-ib must be the zero.

Q: 23. If 3 and (3+3) are two of the roots of a third degree polynomial with integer coefficients,…

A: We have to choose the correct answer from the given option according to the given condition

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

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Q: A quintic polynomial (degree 5) P(x) has rational coefficients. If -3, v2, and 1+i, are roots of…

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Q: Let a, be the leading coefficient. Degree 3, a, = - %3; zeros 1 + i and 4. (a) Find the complete…

A: If a+ib is root of the polynomial then a-ib is also root of the polynomial.

Q: What are all the possible rational roots of the polynomial )= -3r+x-37 1.3 B 1.-1.3.-3 1.-1.2.-2. 3.…

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Q: Find a polynomial P(x) with rational coefficients that has the degree 5 and zeros -2, 1+ 2i and –1 –…

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Q: Find a polynomial with integer coefficients that satisfies the given conditions. P has degree 2 and…

A: The polynomial has degree two so the Highest power of x in P(x) will be 2.  To zeros are, x = 4+i…

Q: For the given polynomial o find the maximum possible numbers of the positive and the negative root.…

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Q: A real and rational polynomial P(x) has the zero of (1 – i) given that i =V-1 is the imaginary…

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Q: All the real roots of a polynomial p(x) of degree nine are listed below. The multiplicity of each…

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Q: A. Complete the table below. Verify that the given numbers in the last column of the table are…

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Q: Find a polynomial P that satisfies all of the following: (i) has degree 5 (ii) has zeros at1/2, −1…

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Q: Consider the polynomial P(r) = 2r+r+5z+5r+3r + 4. (a) Find all possible rational roots of P(r) as…

A: Synthetic division is a method of dividing a polynomial by a linear expression analogues to the…

Q: 2. A polynomial is givenP(x) = x' + 3x² – 36x – 20 a. Use synthetic division and the division…

A: Given:Px=x3+3x2-36x-20

Q: List all possible rational roots. Then use a calculator, synthetic division and factoring to find…

A: Solve the given problem.

Q: Find an nth-degree polynomial the real zeros and the given fur n 3B 3 and 5i are zeros; f (2) = -87

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Q: Find a polynomial with integer coefficients that satisfies the given conditions. P has degree 2 and…

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

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

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Q: Prove that r+ 4r +3 = 0 has eractly one real root using the outline below. (a) Use IVT to prove that…

A: a) Let, f(x)=x5+4x+3 and note that for every x, x is a root of the equation if and only if x is a…

Q: Factor the polynamial completely. Px) - + 40 KN) - Find all its zeros. State the multiplicity of…

A: Given polynomial,         P(x)=x2+49

Q: Let p(x) be a real polynomial of degree 3 (s0, p(x)-ax+ bx+ Cx + a for some real numbers a,b.c,d…

A: Given that p(x) is a polynomial of degree 3.  That means p(x)=ax3+bx2+cx+d for some real numbers a,…

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

A: The roots are -14, 7, 2iTo find other zero

Q: Find a polynomial of degree 4 that has the following zeros: 1, -3, -2i.

A: Complex zeros occur in conjugate pairs. Hence, if -2i is one of the zeroes, hence 2i will also be a…

Q: Find the zeros and fully factor f(x)= x^3 + 5x^2 + 5x + 1 including factors for irrational zeros.…

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Q: Suppose that a polynomial function of degree 5 with rational coefficients have the given numbers as…

A: Given : A polynomial of degree 5 with rational coefficients has roots-12,11 and -5i   To Find :…

Q: actor the polynomial completely. P(x) = x3 + x2 + 9x + 9 P(x) =         Find all its zeros. State…

A: Zeros and multiplicity: - A function's zero is a x-value that gives the function the value 0.The…

Q: (a) Find all the zeros of the polynomial function P(x)=x² +6.x+ 20. Use a graph to help get started.…

A: Explanation of the answer is as follows

Roots

The main dissimilarity between real and complex roots is that the real roots are obtained as real numbers, in contrast with the complex roots, which are indicated as imaginary numbers. The standard format for depicting any complex number is in the form of a + bi.