6. (a) Prove that f(x)=z³-² +2 has no roots in Q.

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

Q: -Find Taylor or Maclaurin for the following functions: 3) 2) f(x) = ex at a = 2 4) f(x) = x³ - 2x +…

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Q: Show that f(x) = x³ − x² − 3x + 1 has a zero over the interval [0, 1].

A: given function We need to sow that function has a zero on given interval.

Q: Let C be a constant. Consider Compute(a) da. ان | دن 3 7 3 73 ㅠ + CT 53 + СT 7 + СT 3 -x², f(x) 2) =…

A:

Q: 1. The goal of this problem is to determine all of the roots of the polynomial f = X²+3X+1 in…

A: According to guidelines we can do only first three sub parts thank you.We have to find the…

Q: 5. Find all polynomials f(x), g(x) satisfying (2x³ + 1) ƒ(x) + (x² + 3x + 1)g(x) = 1 in Z5 [x]. Are…

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Q: (a) Determine whether f(z) = 91³ -21³ +18z-50 is irreducible over R.

A:

Q: 4cos20 + 2/3 = 0 on the interval[0, 3t]

A:

Q: Determine the main base function as one of f(x) = x, f(x) =x², f(x) = Vx , or f(x) = -. 1 а) h(x) —…

A: A)h(x)=x-7The function h(x) is obtained byvertical transformations of 7 units downof f(x)=xThe base…

Q: 3. (a) Find a unit in Z[√2] which is not equal to 1 or -1. Hint: Use 1 (b). (b) (*) Show that Z[√2]…

A: The objective of the question is two-fold. First, we need to find a unit in the ring Z[sqrt(2)] that…

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: The false-position method may have difficulty in finding the root of f(x) = x² − 7.4x + 13.69 0…

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