Find [K : Q], where K = Q(√5,√11), giving detailed reasons for your answer. Further, is X5 – 11 irreducible over Q( √5 ) ? Why, or why not?

Q: The range for  √( 3 - x) is [0, ∞). true or false

A: The given expression is 3-x. Find the range. Range is defined as all possible output of the…

Q: 3. For the function g(x) = x³ – 2x? – 11x + 12, use long division to determine whether each of the…

A: we devide the polynomial by given factor and if we get remainder zero then this given factor is…

Q: For f(x) = (x + 3)*(x – 6)³(x + 5), list each real zero and its multiplicity.

A: Given function is f(x)=x+34x-63x+5

Q: For f(x) = Vx+5 and g(x) = x + 8, the domain of x-9 x is?

A:

Q: 8 Find all zeros. a) f(r) = 23 + 3r? – 4x – 12 b) f(r) = a – 7x4 + 10r3 + 14r² – 24x c) f(r) = r(r –…

A:

Q: If f(x, y) = 2√x² + y² - 16, then the domain of f is the set D = {(x, y)]x² + y² ≥ 4}. Select one:…

A:

Q: . Determine a such that (x – i) is a factor of f(x)= x² + ax – 6.

A:

Q: The interpolating polynomial p(x) of degree 2 of f(x) = 6xª – 2x³ + x² + 9 is p(x) = x² + 9. %3D…

A:

Q: What is the quotient when f(x) = 6x¹ − 2x³ + x² − 3x + 1 is divided by g(x) = x² + x -2 in Z₂[x]?

A:

Q: 16. SKOW thát x – m is a factor of xª – ma for any positive - 17. Use the Factor Theorem to show…

A: 16). Given data:   The given expression is P(x)=xa-ma.   Substitute m for x in the given expression.…

Q: [x(4x²+6)√2x² +3dx = is

A:

Q: Consider the cubic polynomial 2.r + 5x2 –r - 6. a) Given that 2r +3 is a factor, use polynomial…

A:

Q: Give the domain of s(x)=x2+2x√16−5xs(x)=x2+2x16-5x in interval notation

A: Given the functions(x)=x2+2x16−5x

Q: Find the inverse of the functionf(x) = √(r 2 - x2) , 0 ≤ x ≤ r

A: Inverse actual meaning is upside down, and in the function case the meaning of inverse of the…

Q: Find all the zeros. 9) f(x)= x³ + 10x² + 25x + 18 A) -2,-4 +√√7 B) 2, -47i C) -2,-4 ± 7i D) 2,-4 ±…

A: The given equation is; f(x)=x3+10x2+25x+18According to the bartleby guidelines we solve only one…

Q: Find the QR factorization of A = R = Ex: 1.23 0 -1 -4 -2 0 0 3 1 0 given Q 0 -0.24 -0.97 -0.99 -0.12…

A:

Q: 11. Find the domain of √√x-4 x² - 6x f(x)=

A:

Q: ax x(x² - 1)

A: The given integral,       ∫dxxx2-1

Q: Evaluate √+dA, where D is the domain in Figure 4 -R₂ D FIGURE 4 R₁ F: x² + y² = 196 G: (x-7)² + y² =…

A:

Q: function is defined as f(x)=-4+√mx+12 , x is an element of real where x is greater than and equal to…

A:

Q: for what value of m, x²-3mx + m> 0 is proved for any real value of x?

A: Answer

Q: If f(x, y) = 2√√x² + y2 - 16, then the domain of f is the set D = {(x, y) x² + y² ≤ 16}. Select one:…

A:

Q: Determine Q(x) when P(x)=x³-5x2-3x+2 is divided by x-1 and then expressed in the form Select one: O…

A:

Q: 5. а) Factor the polynomial f (x) = 3xª+2x³+2x² +2x-1 into irreducible polynomials in C[r], R[7),…

A: In complex number, .

Q: Given the adjacent figure: A 2x +1 В x +1 ABCD is a rectangle of length (2x + 1) and width (x + 1).…

A: Use the formulas for the area of rectangle and square.

Q: Find || r(t)||. r(t) = √ti + 8tj – 6tk √101-t X

A: Given,

Q: Find the integration distance (f, 9) = | f(x)g(x) dæ between the given polynomials. f(x) = 11æ – 3,…

A:

Q: Let f(x) = x4 − 9x3 + 23x2 − 15x − 10. Find an integer n1 so that f(x) has a root between x = n1 and…

A:

Q: Prove that f(x) = 5x? + 3x – 26 is 0(x²). %3D

A: Given: f(x) = 5x2 + 3x – 26  is  θ(x 2).

Q: (a) What is the degree of Q(7, V3) over Q ? Justify your answer. Is the polynomial X - 5 € QIX)…

A: Degree of extension- Let E be an extension field of a field F i.e. F is a subfield of E, also E is a…

Q: w that : The degree of Q(√√2, √√5) ove least 35. The degree of (√√2, V5) ove most 35. The polynomial…

A:

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

A:

Q: For the polynomials p(x)=4x* – 3x² +x -1 and d(x) =x² – 1, write in the form p(x)= d(x)q(x)+r(x).

A:

Q: Let p(x)-x-5x?+4x-20. Verify that p(5)-0 and find the other roots of p(x)-D0.

A: p(x)= x3 - 5 x2 + 4x -20   Verify that p(5)=0; p(5)= 53- 5*52+4(5)-20 p(5)=0   Hence, x= 5 is one…

Q: Find and draw the domain of m (x, y) = √x-y+√x+y.

A: For a function: z=f(x, y), the set of real values of x, y for which f(x, y) is defined is called the…