Given that 2=l+ 2i and z=1-2i are roots to the polynomial eguation 22-52 cz-S0, wherecER.Fnd the other root and the vake ofc z is and c is

Q: Suppose we factor the polynomial f(x)=(x² – 6x + 9)² · (x² – 4x + 5)³ as much as possible. Choose…

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Q: Find a, b, c E R such that the polynomial f(x) = x³ + ax? + bx + c is divisible by g1(x) = x + 2 and…

A: The remainder theorem says that when a polynomial px is divided by x-a. The remainder is obtained as…

Q: nd the possible roots of the polynomial 2x³ + x4 - 7x² - 8x + 12 e factors of ± by factors of ± 12 1…

A: According to our company's guidelines I can only answer first question since you have asked multiple…

Q: For the polynomial s²+25+p=0, if the value of p is less than 1, then the roots will be

A: s2+2s+p=0, p<1

Q: Given the polynomial P(x) = 2x° + kx² + mx + 6 has a known factor of (x-2). When P(x) is divided by…

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Q: (b) Generalize the remainder theorem to work for lm.d if m 7 0 instead of only l1,-k. In other…

A: b) We want to find the remainder after dividing f by lm,d if m≠0. Where f is a polynomial and lm,d…

Q: Find the zeroes of the polynomials f(x) = x3 -12x2+39x, if it is given that the zeroes are in AP

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Q: The number of zeros of the polynomial x? + 2x +3 in Z, is: 1 None 4.

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Q: Cermine which of the following polynomials is not factorable (prime). A. 2x2 - 7x - 4 В. Зх2 + 2х +1…

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Q: When dividing the polynomial p (t) = 4t° – 17t + 14t – 3 by t - 3, the remainder can be determined…

A: Given;           p(t)=4t3−17t2+14t−3 The objective is to find the value of the remainder by…

Q: Consider the polynomial P (x)=kx' - 5x +3x + 2. Find the value of k such that the remainder is 4…

A: The polynomial is given by Px = kx3-5x2+3x+2 The remainder obtained after dividing the polynomial Px…

Q: (a) Show that r= 3 is a solution of 3z 15+ 17z + 3 = 0. (b) Hence name the theorem that allows us to…

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Q: (a) Construct a table containing the values of the fourth- degree polynomials f(x) = 2x", g(x) = 2r…

A: Given: The functions, f(x) = 2x4g(x) = 2x4-5x2+1h(x) = 2x4+5x2-1k(x) = 2x4-x3+2xx = ±20, ±40, ±60

Q: The number of zeros of the polynomial x? + 4x +1 in z, is: 4 None 1

A: solution of the given problem is below...

Q: Given that z=1+2i and z=1-2i are roots to polynomial 2z^3-5z^2-cz-5=D0, where ER find the other root…

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Q: Consider the polynomial P (x)=kx' + 3x + 4x + 2. 3. 2. %3D Find the value of k such that the…

A: The solution of the problem is given in the next step.

Q: Given that the polynomials has the given roots, find the other roots.   1. F(x)= x^3+5x^2-2x-10.…

A: As you have asked a question containing multiple subparts and not mentioning which subparts to be…

Q: . If we divide the polynomial P by the factor x  c and weobtain the equation P1x2  1x  c2Q1x2 …

A: If we divide the polynomial P by the factor x-c and we obtain the equation Px=x-cQx+Rx, then we say…

Q: Consider a polynomial of the form p(x) = x2(cx4 − 1), where c ̸= 0 is a constant. (a)  What is the…

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Q: A real and rational polynomial P(x) has the zero of (1-√3). Which of the following must be a factor…

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Q: Find a polynomial `P\left(x\right)`which satisfies the following conditions: 1) `P(1+i)=0` 2)…

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Q: Let q represent the degree of the following polynomial 5xym -43y'z'+21. Find the value of q- 2. 19…

A: If a polynomial contains more than one variables then we must add the powers of each variables of…

Q: A polynomial P ( x ) with real coefficients has 5 + 9 i as a zero. What other number must be a zero…

A: Comples zeroes of polynomial always come with conjugate pair. For example if a + b i is zero then a-…

Q: a.) Show that i is a zero of the polynomial x³ – ix? + 2ix + 2. b.) -i is not a zero of the same…

A: a. Consider the given polynomial: Since So, complex number i is one zero of . But

Q: 5. Given the polynomial P(x) = 3x + kx? + mx + 12 has a known factor of (x-3). When P(x) is divided…

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Q: If we divide the polynomial P(x) by the factor x − c and we obtain a remainder of k, then we know…

A: Remainder theorem states that if we divide a polynomial by x-a then the remainder will be fa. Here,…

Q: 2. For 5a + 30z – 40z? + 36x + 14 and c = -7, find P(c) using the Remainder Theorem.

A: we have to find p(c) by using remainder theorem

Q: Determine the number of zeros in the right half-plane (Re z > 0) of the polynomial p(2) = 23 + 22 +…

A: "Since you have asked multiple questions we will solve the first question. For the remaining kindly…

Q: For a fifth order polynomial, if r = a + bi is a root, and r = c+ di is a root, how many real roots…

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Q: Find a, b, c e R such that the polynomial f(x) = x° + ax? + bx + c is divisible by g1(x) = x +2 and…

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Q: Cermine which of the following polynomials is not factorable (prime). A. 2x2 - 7x -4 B. 3x2 + 2x + 1…

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Q: Determine whether the second polynomial is a factor of the first. 4x? + 6x + 46; x- 2 ..... Select…

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Q: Let a(z) = 4z – z + 7, and b(z) = 2z +z?. %3D When dividing a by b, we can find the unique quotient…

A: Given : Polynomials  ax = 4x5 - x3 + 7  bx = 2x5 + x2 By dividing a by b we get a unique quotient…

Q: Assume that the polynomial 7? + bx +c = 0 in which b, cE Z, has two integer solutions. Which one of…

A: We have to equation as - x2 + bx + c = 0.......(1) The above equation (1) is a quadratic equation…

Q: When dividing the polynomial p (t) = 4t° – 17t + 14t - 3 by t- 3, the remainder can be determined by…

A: To determine the remainder by evaluating p(3).

Q: If sun of the Squares zeroes of the quadratic Polynomials f(x)=x2-8x+k is 40.Find K.

A: Given- fx=x2-8x+k and sum of squares of zeros is equal to 40. To find-  The value of k. Concept…

Q: • Consider the polynomial P(x) = x³ – 4x² + ax – 3. Find a if, when P(x) is divided by r +1, the…

A: I am just solving the first  two question (1) Given that the polynomial P(x) = x3-4x2+ax-3 , is…

Q: To find the possible roots of the polynomial 2x³ + x4 - 7x² - 8x + 12 divide factors of + by factors…

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Q: Determine whether the second polynomial is a factor of the first. 4x +3x+34; x-4 Select the correct…

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Q: Q.18 If x– 1 and x + 2 are factors of x +10x + ax+b, then find the values of a and b. If x = 2 and x…

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Q: Rewie the polynomial in the form ax+ bx+c and then identify the val b, and c 9x – a2 8. - - -

A: Identify the value of a,b,c

Q: Construct a polynomial with Z coefficents with a root of the given C 2+ V7 (d) 3 (e) V3+ v2

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Q: 4. Which of the following describes the end behavior of the polynomial y = –x³ + x? %3D as z -oo, y…

A: Here  function is given and we have to find the end behavior of function

Q: Let a(z) = 5z - 6z + 10z - 2, and b(z) = 15z' + 2z. %3D %3D When dividing a by b, we can find the…

A: In this question we have to find q(x).

Q: Find the value of c so that the polynomial p(r) is divisible by (r + 2). p(z) 4x + ca +a + 2 %3D %3=

A: According to the given information it is required to find value of c such that (x+2) divides…

Q: For the polynomial s2+2s+p=0, if the value of p is equal to 1, then the roots will be

A: Putting p=1, to find the roots of s.

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

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Q: 2n b) The polynomial, fW =2x" +mx-3, where m and n are real constants, %3D is divisible by (x+1) but…

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Q: Find a, b, c e R such that the polynomial f(x) = x° + ax? + bx + c is divisible by g1(x) = x +2 and…

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