Find the polynomial with real coefficients of the smallest possible degree for which I and 1+I are zeros and in which the coefficient of the highest power is 1

Q: A fifth degree polynomial with constant coefficients may have (1) 5 distinct real roots. (II) 3…

A: This question can be solved by using the concept of nature of roots of n degree polynomial.

Q: The polynomial f(x)=x^4+6x^3+ax^2-54x+c has four real roots r1, r2, r3, r4 such that r1+r2 = 0 and…

A: The polynomial f(x)=x^4+6x^3+ax^2-54x+c has four real roots r1, r2, r3, r4 such that r1+r2 = 0 and…

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

A: 3+i is a zero, so [x-(3+i)] or (x-3-i) is a factor of P. 3-i is a zero, so [x-(3-i)] or (x-3+i) is a…

Q: A polynomial P is given. (a) Factor P into linear and irreducible quadratic factors with real…

A: (a) part Consider the given polynomial  Px=x4+8x2+16 Now, write the polynomial into linear and…

Q: 3. Let p(x) = 6xª – 13x³ + 13x² – 2. - (a) Find q(x) such that p(x) = (2x – 1)q(x) using synthetic…

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Q: A polynomial is known to have the following roots x₁ = 4.9+ -4.3 i x2 = 2.3 x3 = (4.6) ¹/2 Determine…

A: If the root is complex number of a real coefficients polynomial then it has complex conjugate root.…

Q: Find a polynomial with integer coefficients that satisfies the given conditions. R has degree 4 and…

A: Given: R has degree 4 and zeros 3 - 4i and 4, with 4 a zero of multiplicity 2.

Q: A polynomial P is given. (a) Factor P into linear and irreducible quadratic factors with real…

A: To factor the given polynomial

Q: The positive value of k for which x2 +kx+64=0 & x2 -8x+k=0 will have real roots

A: Given the quadartic equations(1)x2+kx+64=0(2)x2−8x+k=0

Q: Factor the polynomial 4x 4-28x 3+ 61 x2 - 42x+9 and find its zeros given that one of its zeros (of…

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Q: find a polynomial with integer coefficients that satisfies the given conditions.  R has degree 4…

A: Given problem:- find a polynomial with integer coefficients that satisfies the given conditions.  R…

Q: 9. The polynomial 12 + kv -6 has 2x I as one of its factors. Determine the value of k.

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Q: There is the positive real roots of a family of polynomials of the form: p(n) = x^n - x^(n-1) - ...…

A: We will use basic arithmetic to solve this equation and besides this the knowledge of plotting the…

Q: find a formula for the polynomial p(x) with degree 3 leading coefficient 1 zeros at 3, -5, and 8

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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: Express the second order polynomial p(x) = x^2 + 4x + 13 in the sum of square form. a. (x+2)^ 2 -…

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Q: A polynomial P is given. P(x) = x^3 - 3x^2 + 4x - 12 (a) Factor P into linear and irreducible…

A: Given that:p(x)=x3-3x2+4x-12

Q: A polynomial P is given. P(x) = x6 − 64 (a) Factor P into linear and irreducible quadratic factors…

A: The given polynomial P is,

Q: A complex polynomial function f of degree 4 with real coefficients has the zeros - 1, 2, and 3 - i.…

A: A complex polynomial function of degree n has n zeros. Multiplying a polynomial by a constant does…

Q: A fourth degree polynomial with constant coefficients may have (1) 4 distinct real roots. (1I) 3…

A: Topic:- polynomial

Q: the polynomial function P has real coefficients and if a + bi is a zero of P, then is also a zero of…

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Q: Find a polynomial with integer coefficients that satisfies the given conditions. Q has degree 3 and…

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Q: Find a polynomial with real coefficients, degree 3, and zeros 3 − 2? and −2. Give both the factored…

A: Given, degree=3 zeros are 3,-2, and -2.

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: Find a polynomial with integer coefficients that satisfies the given conditions. Q has degree 3 and…

A: To determine the expression for a polynomial satisfying the given conditions

Q: Give a valid reason why this polynomial is irreducible over the rational numbers: X°-3. There is…

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Q: 11. Rewrite the polynomial in Standard Form: 12-3x- 10x -x2 O b) 3x³ - x² +10x + 12 O a). 3x3-…

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Q: Find a polynomial P(x) of degree 3 that has integer coefficients and zeros 1/2 and 3 - i.

A: 3-i+32+1=-i2+1=-1+1=0 So 3-i  is a zero of " x+32+1 ". . . . . . (1). 2·12-1=1-1=0 So 12 is a zero…

Q: Give a polynomial of degree 3 that has zeros of 18, 10i, and –10i, an the polynomial in standard…

A: Given that: Zeroes of the polynomial = 18, 10i and -10i and At x=1, y=-3434.

Q: 5. What are the real and complex solutions of the polynomial equation 3-8=0 O1+i3, and 1 –i 02, -1…

A: we know that the expansion of       a3-b3=(a-b) (a2+ab+b2) now put the value in it and get

Q: How do I form a polynomial from the zeroes 5, -i, and -2+i with a degree of 5. I am very confused as…

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Q: 2

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Q: 2. Find a polynomial with integer coefficients that has degree 3 and zeros 3, 2i, -2i.

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Q: and 21. 27. A fourth degree polynomial, P(x), with real coefficients has 4 distinct zeroes. Two of…

A: As per the Bartleby guidelines we are supposed  to answer only 1question per post. This post…

Q: 11. If æª +4a12³ +6aza² +4a3x +a4 = 0 is an equation with real coefficients and has two real and two…

A: The roots are concyclic or the roots are at the same distance from the origin, and the given…

Q: Find a polynomial with integer coefficients that satisfies the given conditions. Q has degree 3 and…

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

A: Given,         P has degree 2 and zeros 2+i and 2-i.

Q: a) Show that x = 1+2i is a root of p(x) where i = surds(-1). b) By using the fact that p(x) is a…

A: We have to solve given problem:

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

A: Given that the zeros of polynomial are 1 + i and 1 - i. To find the polynomial of P(x) has degree.

Q: 4. If the polynomial function P has real coefficients and if a + bi is a zero of P, then is also a…

A: We know, complex roots occurs in conjugate pairs. So if,x+iy, is a root of given polynomial…

Q: The positive value of k for which x2+kx+64=0 & x2-8x+k=0 will have real roots

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Q: A polynomial P is given. P(x) = x - 2 + 4x - 8 (a) Factor P into linear and irreducible quadratic…

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Q: Find a polynomial with integer coefficients that satisfies the given conditions. Q has degree 3 and…

A: Here we have to find the polynomial with integer coefficients that satisfies the given conditions. Q…

Q: The ________ ________ of ________ states that if f(x) is a polynomial of degree n (n > 0), then f…

A: The ________ ________ of ________ states that if f(x) is a polynomial of degree n (n > 0), then f…

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

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Q: Find a polynomial with integer coefficients that satisfies the given conditions. R has degree 4 and…

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Q: Find a third-degree polynomial that has integer coefficients and zeros and 3+i. Evaluate (V12 - V-3)…

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Q: 2. Find the sum of the coefficients of the polynomial obtained by fully expanding (x - 2). С. 1 А.-2…

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Q: 1. Find the third-degree polynomial P such that two of the zeros are 4 and 1 + i and such that P (2)…

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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.