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: Let f(x) = x + √2x3 + x. Verify whether f[0, 1, 2, 3, 4] = f [0, 1, л, е, -1].

A: The details solution of the given question is given below in step 2.

Q: Consider the function h(x) = e³ (x-7) with x E [-7,7]. %3D Consider n + 1 points xo < x1 < ... < x,…

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Q: 2. Let P(x) = ax² + bx + c be an irreducible polynomial in Q[x). Prove that (a) P(x) has two…

A: Let P(x)=ax2+bx+c be an irreducible polynomial in Q[x] a) To show P(x) has two distinct roots, let…

Q: 6) Given e>0 and fe (a) C(0,1) (b) C[-1,1] (e) a or b (d) C2m. There exist an algebraic polynomial P…

A: (Solving the first question as per our guidelines) Solution: We know that For each f∈C0,1 there is a…

Q: Find the third Maclaurin polynomial to f(x) = e sinx

A: The Maclaurin series; fx=fa+f'a1!x-a+f''a2!x-a2+f'''a3!x-a3+.... Where the center is at x=a=0…

Q: Let f(r) = (8+2)r Find the third Maclaurin polynomial for f. Use the polynomial in (a) to evaluate…

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Q: Find a monic polynomial of least degree in R[x] that has 1-i and 2i as roots. write the powers of x…

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Q: Let f(x)= x³ + 2x+ 1 and g(x)= 4x + 1 be two polynomials in a ring (Zs[x],+ ,.). Find q(x) and r(x).

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Q: Q5 (i) Prove that the chromatic polynomial of K2_s is (ii) Prove that the chromatic polynomial of Cn…

A: Solutions

Q: Given the polynomial f(x) = -2x7 + 4x³ + 4.x³ following) а) 10 determine the end behavior of f…

A: see the attached file for a step-by-step explanation of end of the behavior of a function 'f'.

Q: Form the interpolating polynomial of degree k that satisfies pG) (xo) = f(G) (xo) for 0<j< k.

A: To form: The interpolating polynomial of degree k that satisfies pjx0=fjx0 for 0≤j≤k

Q: Q2) Find the expansion in Legendre polynomials of the functions: a) f(x)=2-x-x² x) = { 1 ) 0, b)…

A: We have to find the expansion in Legendre polynomials of the function.

Q: Use appropriate Lagrange interpolating polynomials to approximate f(1) if f(0) = 0, f(2) = −1, f(3)…

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Q: The coordinates of the P(x)=x³ – 2x2 + 3x polynomial with respect to the base B-[1, x, x?,x'] are as…

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Q: Let f(z) be an entire function satisfying |ƒ (²1 +22)| ≤ |ƒ (2₁)| + + + |ƒ (2₂) | = n for all 2₁, 22…

A: As per the question we are given an entire function which satisfies the following inequality :And…

Q: Express K (x) in terms of the orthonormal Legendre's polynomials, with the inner product. Here, K(x)…

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Q: Explain Hermite Polynomials for Generating Function?

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Q: let f(z) be polynomial of degree at least two. show that |f(z)|>|z| for large |Z|.

A: We prove this result by contradiction.

Q: Show that there are no polynomials f(x) and g(x) in Z[x] such that 1 = 2f(x) + xg(x)

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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: Suppose f(z) is an analytic function with domain C (the set of all complex numbers). Suppose further…

A: Suppose further that in the region {|z| &gt; 100} f satisfies f(Z)&lt;a+ b |z|^n where a ,b are…

Q: Find the recursion formula and a fourth degree polynomial approximadion for the power serîies…

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Q: The real zeros of the quintic polynomial f (x)=x' – 3xr' – 27x² +81 are: {-V5,0, V5}. d.…

A: Given polynomial is fx=x5−3x3−27x2+81 We have to find the real zeros of the polynomial…

Q: 2. Let char F = 0 and f(x) E F[x] be a monic polynomial having positive degree. If d(x) = gcd(f(x),…

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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.

Q: Q3: Factorize f (x) = 2x* + x³ + 2x + 4 € Z5[x] as a polynomials product to irreducible over Z5?

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Q: Let plx) be the Lagrange interpolating polynomial that C-2,3), (2,4), (4,3) Aits the data the n P(3)…

A: See the attachment

Q: an

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Q: 9iven Poly nomial y (x) = 2x° +x-13x+ 6 Pioue that ½ is a root of the Ke polynomial nthe fiz…

A: Given that 2x3+x2-13x+6 find the roots of the given polynomial . show that one of the root is 1/2.

Q: Given a positive integer d, define Q[vā] = {s(Va) : f € Q-]}. i.e. the set of real numbers that can…

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Q: 3. Is the polynomial f(x) = 2x° + 30r – 150 € Q(r] reducible or irreducible over Q? In either case,…

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