2. Using known theorems prove that P(ANB) > P(A) +P(B) - 1

Q: 3. Let f(2)= and let C = {2 € C : |2| = 1}, described in the positive sense. Determine the value of…

A: 3. Given function as f(z)=z4-5z2 and C=z∈ℂ:z=1

Q: Given the function P(n) = (n – 2)( – 5n + 6)°(n – 3)°, - its roots are and their multiplicities are

A:

Q: i. Suppose p is an irreducible polynomial of degree n with coefficients in Q. Then p has

A: Determine whether p(x) = x3+x+1 is irreducible over  Sol: we know that , let f(x) be a polynomial in…

Q: Factor x^3+x+1 over Z3

A: We have to factorize the polynomial x3+x+1 over Z3. Take px=x3+x+1. Note that, Z3=0, 1, 2 and the…

Q: B = {1 + x + x, x + x2, x2}. for P2. Let p(x) = 2+x + 2x?. Then [p(x)]3 : %3D %3D 2 - 1

A: Using linear combination of three polynomials

Q: 5) Find the general form of the funclion f(x), given that f"(x) = X+1, f(0)=1, and f'C(6)= -1

A: The solution are next step

Q: Find a polynomial of degree n=3 that has the given zero(s) x = −2, 6

A: A polynomial is an expression comprised of variables, their coefficients, constant, and exponents,…

Q: Find the 3rd degree interpolating polynomial by Newton's backward formula X f(X) Af(X;) A²f(X;)…

A:

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: If p(x) is a polynomial of degree 8, then p(x) is ze O True

A:

Q: Let f(x)= x* +2.x-ax2 +bx (i) Find the values of a and b so that the multiplici ty of the root 1 of…

A: Polynomial Factorization: A polynomial can be written as a product of two or more polynomials of…

Q: , Consider the interpolating polynomial for f(x) =x² based on th points (0,0). (1,1) and (2,8). Find…

A:

Q: 25. Find a polynomial q e P2(R) such that p(x)(сos TTx) dx p(x)q(x) dx for every p E P2(R).

A:

Q: Find a polynomial of degree n=2 that has the given zero(s) x = −3

A: Let us find a polynomial with a degree of 2 and a zero x=-3 A factored polynomial with a zero -3 has…

Q: Find a second-degree polynomial P such that  P(1) = 1, P'(1) = 2,  and  P''(1) = 6.   P(x) =

A:

Q: Let X have the pmf p(x) = (12 )x, x = 1, 2, 3, . . ., zero elsewhere. Find thepmf of Y = X3.

A: We will use the following :  Discrete random variable X is variable which has finite or countable…

Q: Find a polynomial of degree n=4 that has the given zero(s) x = −4, −1

A: Find a polynomial of degree n=4 that has the given zero(s) x = −4, −1

Q: Evaluate the sum of f(x) Ax, with x, = 0, x2 = 2, X3 = 4, X4 = 6 i=1

A: Given,     ∑i=14f(xi)∆x=?Where    x1=0, x2=2, x3=4, x4=6, and ∆x=2,            f(x)=3x-1

Q: Find a polynomial of degree n=2 that has the given zero(s) x = −√2, √2

A: Find a polynomial of degree n=2 that has the given zero(s) x = −√2, √2

Q: 4. Consider the polynomial f(x) = x² + 1. (a) Show that f(x) is irreducible in (Z/3Z) [x]. (b) Show…

A:

Q: Let x be defined as x = x² -x + 1 for all values of x. If p = p -3, what is the value of p? A 1 BO…

A:

Q: Prove that you can find a polynomial p(x) = Ax2 + Bx + C that passes through any three points (x1,…

A: we have to prove that we can always find a polynomial p(x) = Ax2 + Bx + C that  passes through any…

Q: Using Taylor's theorem, formally represent 2x° +x* – 3x³ +x² – 5x +1 as x+1.

A:

Q: Determine the zero(s) of m(x) = 7 – 3x. x =

A: The equation is given by mx = 7-3x                                       ........1 To evaluate: The…

Q: Find a polynomial P(x) = x' + ax² + bx + c satisfying all the following properties 1) P(0) = 0 2) x…

A: Given form of polynomial,  P(x) = x3 + ax2 + bx + c To find the polynomial which follows below…

Q: When applying the convolution theorem to calculate: a 8 L-1 ¹ { x² + Q² * x² +F}" You obtain the…

A:

Q: The minimum polynomial of 5'3 over Q is x 1/3

A:

Q: et x be the number of red balls among 3 balls randomly selected from a bag containing 9 black ball…

A: Given that  x = The number of red balls among 3 balls randomly selected from bag. Number of black…

Q: Let f(x)=√x-x² and P2(x) be the interpolation polynomial on x=0, x, and x = 1. Find the largest…

A:

Q: 5. Obtain a polynomial P(x) such that f(x) = P₁(x) given the table -1 -3 x₁ f(x₂) -2 -13 1 -1 2 -9 3…

A:

Q: the degree of homogeneity, if there is one, for eac 1 X1,X2, X3) = - xf +x +x X2 X3 O gro finotion:…

A: Introduction: For a function f(x,y), the degree of homogeneity is an integer n such that,…

Q: 3.2 Determine if the following statements are true or false.. Give reason for your answer, also…

A:

Q: If g(y) is differentiable for 2<_y<_3 (<_ means less than or equal) and g(2) =g(3)=-1, then there is…

A: There is one theorem i.e. Rolle's theorem states that if a function f is continuous on the closed…

Q: c) Prove that there cannot exist two different polynomials q,r E K[x], both of degree less than n,…

A:

Q: 12. R sed e A fourth-degree polynomial P(x) satisfies A4P(0) AP(x) = P(x + 1) - P(x). Compute…

A:

Q: a) Factor a + r³ + x into irreducible polynomials in Z2[x];

A: We shall solve first Que only, if you want others to be solved kindly post it again by mentioning…

Q: Let f(x) = 1+ + x² + x³ + x4 +x5. Find the remainder R3(x) = f(x) – T3(x). Find the maximum value of…

A: Given:Let f(x) = 1+x+x2+x3+x4+x5

Q: Q1(i) Prove that Lim + a+ 1 2n²+1 V2n²+2 V2n²+n]

A: (1) Given, g(x)=limn→∞12n2+1+12n2+2+.....+12n2+n suppose any f(x) and g(x)…

Q: of both P(x) and P(x)÷(x-r) P(x)= x4+2x2+8x+5; r=-1

A: if (x-r) is a factor of p(x) and p(x)÷(x-r) then when we divide both by (x-r) the remainder will be…

Q: 8. In Newton-cotes formula, if f(x) is interpolated at equally spaced nodes by a polynomial of…

A: To find- In Newton-Cotes formula, if fx is interpolated at equally spaced nodes by a polynomial of…

Q: express the quotient  P(x)/D(x)  in the form  P(x) D(x) = Q(x) +  R(x) D(x). P(x) = 8x2 − 3x − 17,…

A:

Q: 17. Find the solution to the interpolation problem of finding a polynomial q (x) with deg(q) < 2 and…

A:

Q: 7. Let z be a root of the polynomial p(z) = (z + 1)" + z". Show that %3D 1 Re z = - 2

A: For the solution follow the next step.

Q: C. Use the Golden Section method to solve the minimum of f(x) = In(x²) + In (x³) + In(x*) using an…

A: Given f(x)=ln(x2)+ln(x3)+ln(x4) xi=0.2xu=4

Q: 8. Consider the function f(x). f (x) = x3 + x2 – 26x – 30 - а. What is the degree? b. What is the…

A:

Q: 2. Prove that a function which is analytic in the whole plane and satisfies an inequality |f(2)| <…

A:

Q: {1 + x + x, x + x², for P2. Let >(x) = p(x)]B = 1 + 3x + 2x2. The

A: Here we have, B=1+x+x2, x+x2, x2  for P2. Let p(x)=1+3x+2x2 We have to find, p(x)B=?