Let T: P₂- R² be defined by +T (PO) = [PⓇ]. (a) Find a polynomial p(t) in P₂ that spans the kernel of T. (b). Find a polynomial g(1) in P, such that 7 (q(1)) = [4] · P

Q: Compute the convolution L ★ II of the functions L and II, which are defined below: 1 if |æ| <a/2…

A: For the function, Lx and πx, Convolution of Lx and πx can be calculated by L∗πx=∫0x Lt πx-t…

Q: 3) Let f(T) e R[T] be a polynomial of degree > 3. Show that there exists polynomials g(T) and h(T)…

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Q: Let R[x] be the set of all polynomials with real coefficients. In other words, x] = {anx" + an-1x"-1…

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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: 2. Consider the Newton polynomial Pn(z)= ao+a1 (1-10) + a₂(1-10) (1-11)+... +an(1-10)(1-1₁).…

A: Given that   that interpolate then we have Now  ,       putting

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A: To prove that 2^(2/3) + gamma is a primitive element of Q(gamma, 2^(2/3))/Q, we need to show that it…

Q: The function g defined by g(z) = 23 (z − (1 + i))³ - has a pole at the point z = 1+ i. State the…

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Q: Define T:P,-R as shown to the right. P(- 1) a. Find the image under T of p(t) = - 2-t b. Show that…

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Q: 2) Let f(T) e Q[T] be an irreducible polynomial of degree n > 1. Show that f(T) has n different…

A: We will use the basic knowledge of ring theory to answer this question properly, in detail.

Q: Let p: R → R be a polynomial of odd degrees. Prove that the equation p(x) = 0 has a solution in real…

A: Given p:R→R be a polynomial of odd degree. We have to prove that the equation px=0 has a solution in…

Q: 2. Consider the Newton polynomial Pn(x) = ao+a1(xr-xo) + a₂(x-xo)(x − x₁) +... +an(x-xo)(x -…

A: Given that   that interpolate then we have Now  ,       putting

Q: Show that f(x)= x14 – 6x + 75 is irreducible over Q.

A: Eisenstein's Irreducibility Criterion: Let us consider polynomial…

Q: ƒ(X) e F[X] be a non-constant polynomial of degree d. Prove that f(a) has degree at least over F.

A: ANSWER :

Q: Let f(r) = x – 8rš. (a) Prove that f has a maximum and minimum value on [0,4]. (b) Find the maximum…

A: Here we have to find the maximum and minimum value of the given function.

Q: Find kernel(T) and range(T): T (ED) || [1 3 2] 0 1 1 1 2 1 10 1 3 1 2 X 2

A: