Show that Q(√5 + √5) is Galois over Q and determine the Galois group.

Q: Please explain how the square root property is related to the difference of squares.

A: The square root property says: If x2=a then, taking square roots, x2=a     x=±a Now, solving the…

Q: Question 2-11 The area of a throw rug can be represented by the expression 2x^(2)+5x-12. Which of…

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Q: Thank you! I am a bit lost because the equations are a bit messy with the computer. Would it be 3e^x…

A: GIven function :- y=3ex+8x3

Q: Need help with this calculus question, please do all. Thanks.

A: We are given a 3rd degree polynomial, of which we need to integrate from -2 to 2. Also, we are…

Q: Not sure how to start this  x^2=8x+4 Completing the square  x=

A: Given  x2=8x+4 Solve the equation by completing the square method x2=8x+4subtract 8x from both…

Q: (X+5)^2 I need to write this in a punnet square format please help

A: Punnet square format of (x+5) ^2

Q: how did you find the root zeros

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Q: the area of the windscreen of a bus is 1.21m^2. In a photograph of the graph, the windscreen appears…

A: Given: The area of the windscreen of a bus is 1.21 m^2. In a photograph of the bus, the windscreen…

Q: how to derive: cube root of x over x minus 6.

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Q: 2, i, Find out the roots of the following by completing the square. 5x^2-2х-4-0

A: To Find: the roots of the following by completing the square: 5x2-2x-4=0.

Q: discriminate

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Q: show that the equation x^5+2x^3+3x-4=0 has exactly one root. Justify your answer.

A: Given equation has only one root. Here is its explanation.

Q: Explain why the polynomial equation 2x^10 +5x^ 6 +x ^4 +19x^2 +1=0 has no real roots.

A: the polynomial equation 2x^10 +5x^ 6 +x ^4 +19x^2 +1=0

Q: rectangle with an area of (2x2-x2-30x+8) and width of (x-4)  finf the length?

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Q: The level of the root is defined to be zero TRUE OR FALSE

A: See the detailed solution below.

Q: What is this quadratic in vertex form? Please show solving steps

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Q: The polynomial x^3-7x+c, where C is a real number, has roots of 1 and -3. Find the third root

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Q: What can be said about Col(A) if A is 20×17? Could it be equal to R^20? Be as detailed as possible

A: Consider the given question, Matrix A is A20x17 .The number of rows and columns in the matrix A is…