Problem Let a = V3+ v7. (a) Find a degree 6 monic polynomial in Q[x] having a as a root. (b) Prove that your polynomial from (a) is the minimal polynomial of a over Q.

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: A monic cubic polynomial has zeros 2 and (-1)/2±√11/2 i. Find the polynomial.

A: Given zeros are 2, -12±112i let a=-2, b=-12+112i, c=-12-112i let x be the variable of the…

Q: An operator whose minimal polynomial is different from its characteristic polynomial

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Q: Which of the following is a polynomial f(x) of degree 3 with real coefficients which

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Q: 49) Let P(z) = ao + a1z +……. 1 order n at o∞. Consider + anz" be a polynomial of degree n. Show that…

A: Given that Pz=a0+a1z+a2z2+⋯+anzn be a polynomial of degree n.Then, an≠0. We have to show that 1P(z)…

Q: Show that u = √3+ √2i is algebraic over Q and type its minimal polynomial p(x) = irr(u, Q) below.

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Q: Let f(r) be a polynomial function such that f"(x) = xª – 5z + 6z². Find the æ values for the…

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Q: Let f(x) = x' + 2x + 4 and g(x) - 3x + 2 in Z,[x]. Then, upon dividing f(x) by glx), we get 7- The…

A: I am solving part7 & part8 as you mentioned.

Q: Determine a polynomial p(x) of degree 2 having zeros −5 and 7

A: The problem is asking us to find a polynomial of degree 2 that has zeros at -5 and 7. In other…

Q: About irreducible polynomials over GF(2) a) How many irreducible polynomials of degree 2 over GF(2)…

A: here we can simply check by putting the value because it has very less number of elements.