Check the definiteness of the following quadratic form;

Q: Consider nonnegative integer solutions of the equation xi + x2 + x3 + x4 + x5 + æ6 = 30.

A: The non-negative integer equation is x1+x2+x3+x4+x5+x6=30Since ,xi-number varying from 0 to…

Q: 1. Which of the following is a quadratic equation? [NCERT Exem (a) x2 + 2x + 1 = (4-x) + 3 (b)- 2x…

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Q: Check the definiteness of the following quadratic form; Q(x1, X2, X3) = 2xỉ + 3x – xỉ + 5x,x3 + x,X3

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Q: Find a counterexample to disprove the conjecture: "The square of a number is always greater than…

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Q: Suppose a quadratic equation is given as follows: (k – 1)x? + x + 1=0 Select all values of k for…

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Q: Show that the square of any positive Integer is of the form 3m or 3m+1 for some integer m

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Q: What is a simple mathematical proof that the square root of 2 is irrational

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Q: give all the possible roots of x4+2x3-7x2-8x+12

A: Give all the possible roots of x4+2x3-7x2-8x+12

Q: Show that the square of any integer is of the form 3m or 3m+1 but not of form 3m+2.

A: Proof :-

Q: Solve the following quadratic equati ons by factorization x+3 1-x 17 (ii) X-2

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Q: Is there a real number whose square is –1? a. Is there a real number x such that _? such that x =…

A: In general, there does not exist any such real number whose square is a negative real number. Hence,…

Q: Prove the statement if it is true, and give a counterexample if it is not true. a. For every real…

A: Both the subparts are solved with explanation.

Q: Which quadratic has zeroes of 5 and 5/2  A) (q + 5)(5q + 2) B) (q - 5)(2q - 5) C) (q - 5)(5q - 2)…

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Q: Solve the following quadratic equation for all values of x in simplest form. (3x – 1)2 – 49 = –13 -

A: Given : 3x-12-49 = -13

Q: Given that α and β are the roots of the quadratic equation ax2 + bx + c = 0. Show that αβb2 = ac(α…

A: Answer

Q: Give an example of each of the following. a. A simple linear factor b. A repeated linear factor c. A…

A: Given: a)  Find a simple linear factorb)  Find a repeated linear factorc)  Find a simple irreducible…

Q: Given that each of the following quadratic equations has no real roots, find the Pange of kx² - 4x +…

A: General form of quadratic equation:ax2+bx+c=0Quadratic Formula:x=-b±b2-4ac2ab2-4ac=0    one real…

Q: Find all the values of m such that the equation mx² – 2 (m + 2) x + m + 2 = 0 has two real roots

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Q: The square root property indicates that if x2= k, then x = __________.

A: According to the given information it is required to tell that:The square root property indicates…

Q: Solve by using the quadratic formula: x +10x+9 =0 O A. 5+4i and 5-4i O B. -5+4i and -5-4i O C. 4+5i…

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Q: Solve the following quadratic for all values of x in simplest a+bi form. x +18x+38 = 4x – 20

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Q: Determine whether the following statement is true or false: T $ {x|x is an irrational number}.

A: π∉x x is an irrational number.

Q: Prove that if æ is a real number, then [2a] = [x] +

A: If x is a real number then  to prove- 2x=x+x+12 Greatest integer function is denoted by [x] for any…

Q: How do you prove the cube root of two is irrational?

A: this prove done by contradiction

Q: If a is a non-real complex nth root of unity, find the values of:

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Q: Suppose that m andn are positive integers and b is a real number so that the principal n" root of b…

A: We have been given that nth root of b exists where b is the real number.

Q: 2. The roots of a quadratic are x = -5 and x = 3. Which of the following are possible factors of the…

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Q: If a, b, and c are constructible, show that the real roots of ax2 + bx  + care constructible.

A: Given Data The quadratic equation is ax²+bx+c.   The a, b, and c are constructible. If a=0, The root…

Q: Do not use a calculator in this question. Find the positive value of x for which (4 + V5)x² + (2 –…

A: 3 Given equation is 4+5x2+2−5x−1=0. We have to find the positive value of x. The solution of the…

Q: Prove by contradiction that if 3x? 2 is irrational then r is irrational.

A: We have to show that x is irrational if 3x2-25 is irrational. We have to prove the statement by…

Q: Find the number of primitive 8th roots of unity in GF(9) .

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Q: Create a question covering the following topics; 1. Inequality( quadratic) 2. Equation ( cubic…

A: Inequality is a mathematical expression that compares the algebraic terms on the two sides of the…

Q: -termined coefficients were used. No need to actually compute the parti ne constants by plugging in.…

A: Given                                  x''-2x'+x=t2et

Q: If o is an imaginary cube root of unity ,Prove 1 1 1 1+20 2+ @ 1+@

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Q: 6 of 12 9.3b | Use the discriminant to predict the number of solutions of a quadratic equation Use…

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Q: |Use the method of proof by contradiction to prove that 3 – V7 is irrational. (Hint: you can use the…

A: rational number  can be expressed as the quotient or fraction a/b of two integers.

Q: The solutions of the quadratic equation x(4x – 3) + 3 = 0 are - O None of these O 3±iv57 8. O…

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Q: Find all the real cube roots of-216.

A: A cube root of —216 is a solution of the equation  x3 = —216 Now, x3 + 216 = 0 x3 + (6×6×6) = 0 x3 +…

Q: Prove the given statement: The sum of the squares of two odd integers cannot be a perfect square.

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Q: If a, b, c are integer powers of 2, prove that equation a° + 64 .3 + 64 = c5

A: Given: Let's take a,b,c are integer powers of 2. Prove that a3+b4 =c5  does not have a solution.

Q: Prove that if one root of ax? + bx + c = 0 is twice the other then 2b = 9ac

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Q: Show that the real number V2- 2 is algebraic.

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Q: Prove that if x is a real number, then [2r] = [r] + r+

A: Let us consider x=n+∈     (Because x is a real number) where n is integer part and ∈ is fractional…

Q: O Prove that V5 is irrational. (ie. explain why complete

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Q: The product rule for square roots states that if a and b are nonnegative, then √ab =______.

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Q: Which of the following are the (solutions) of the quadratic belo x2 -9x +8 O(x-1)(x-8) O (x+1)(x+9)…

A: We have to find the root of the quadratic equations

Q: Solve the following quadratic equati ons by factorization method

A: II)x+3x-2-1-xx=174

Q: (i) q(x) = 3x2 + 2xy +5yz + 7y2 – 2z2 %3D -

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Q: Based on the inputs to the quadratic formula below, how many real solutions are there to the…

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