Let ſa]denote the greatest integer less than or equal to a.Given that the quadratic equation x? + a? - 5a + b + 4 x +b = 0 has roots - 5 [a² %3D and 1.Find all the values of a.

Q: The number of integer values of m, for which the x-co- ordinate of the point of intersection of the…

A: Introduction :

Q: Solve for X such that 2XT - A = B + (CI)", where 21 3 -1 A =|-1 5, B = 2 2 -3 and C = -2 3 10 1. -7…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: For which values of a and m does ax = 1 have a solution in Zm?

A: Claim:

Q: Prove the following equations

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

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: Use the given LU factorization to find all solutions to Ax = b 0 5 1 0 0 15 A = 4 1 0 0 -2 |, b 54…

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Q: Find the root(s) of the quadratic equation O(4. -5) O (2. 6) O (-2, -3) O (1. 5) -6x +5 0

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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: Prove or give an counterexample to the statement that for any neZ+ and aeZn, the equation +n X = a…

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Q: Show that [o 2] A 3 0 has no A = L-U factorization where L is lower triangular and U is upper…

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Q: B. If AC = x + 11, and AB = 24 solve for x. %3D

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Q: If p(q=r) prove that x +q{r-p}x+p-q) = 0 has equal roots, ther 211 q = р

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Q: x is even and v is any integer, then their produc

A: If x is even then x=2m where m is any integer y is any integer,  Case I Let y be even y=2n where n…

Q: Find the value of ‘v’ in v2 – 2v -15 = 0, if v is a natural number.

A: Given quadratic equation is,

Q: If a, b, c are integer powers of 2, prove that equation a + 64 = does not have solution, otherwise…

A: Given: Let a,b,c are integer powers of 2 .

Q: B. Verify if the given values of x are solutions to the equations/ ined 1. 7x + 2 = 9 2. 3x-5 4 srps…

A: 1. 7x+2=92. 3x-5=43. x+8<64. -4x≥15. 3x+1≥7

Q: Find all integer solutions r, y,p to the equation I+y+x² + y? = p such that p is a prime number.

A: In this equation, two integers and their squares are added on the LHS. Squares of integers are…

Q: Solve the following equations in Z6 with x expressed in both standard and non-standard names: (i) xx…

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Q: Find all the solutions r E Ziz to the equation r³ – 5x² – 7x = 0 mod 13.

A: First, solve in real number then ring down to the finite field.

Q: If w and af are the nonreal cube roots of unity and [1/(a + c)] + [1/(b + w)] + [1/(c + w)] = 2w²…

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Q: If the roots of equation x² - 2cx + ab = 0 are real and unequal, - then prove that the roots of x²…

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Q: Given that 1 is a double root of q (x)=4x4-15x³+16x²– Chapter 3x-2, find all roots. All the roots of…

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Q: Prove that if b+ 6 < 0, then x + bx + 5= 0 has at least one real solution.

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Q: Solve for u, where u is a real number, 4√u = 2, if there is more than one solution, seperate with…

A: To determine: The value of u, where u is a real number, 4√u = 2

Q: show that x'-15x +C= O has at most root on E2,2] one

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Q: (2) Determine k such kx? – 4x +÷= 0 that has real and different solutions. 2

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Q: Exercise 6: Consider the equation x" + ax + b = 0, with n E N. Show that the equation has at most…

A: First of all consider f(x) as x^n +ax + b.Then we need to differentiate f(x) w.r.t. x and get f…

Q: and such that the sum of their squares is as small as possible. Give the sum of the squares.

A: Given problem:- 2. Using Lagrange multipliers, find three positive numbers whose sum is 18 and such…

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: Show that the equation In(x + 1) = In(x²) has at least two real solutions.

A: we need to show that ln(x+1)=ln(x2) has at least  two real solutions.

Q: For which values of a and m does ax = 1 have a solutionin Z m?

A: To find for which values of a and m does ax=1 have a solution in Zm. Zm=0,1,2,....,m-1 when a=0,…

Q: Find the complete or particular solution of the following diffi- rential equations:

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Q: Show that if p, q, r and s are real number and pr = 2 (q + s),then at least one of the equations x…

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

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Q: 23. Use the quadratic formula to find all solutions in the interval 0° ses360° to the nearest tenth…

A: “Since you have asked multiple questions in a single request, we will be answering only the 1st…

Q: Solve for x, where x is a real number. 7x+39 x+30 =3 - (If there is more than one solution, separate…

A: Given equation7x+39-x+30=3We have to solve for x , where x is real number .

Q: If the roots of equation x² - 2cx + ab = 0 are real and unequal, then prove that the roots of x²…

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Q: Prove that there are no solutions in integers x and y to the equation 2x2 + 5y² = 14.

A: Two different proofs are given for the given problem as follows :

Q: Advanced Math Question

A: To answer the given question we shall use the following rule. Descartes' Rule: The number of…

Q: Solve for x in x² + 12 < 7x. а. b. Find all possible values of x if one of the interior angles of a…

A: Given query is to find the value of x .

Q: Suppose A is 1x4, B is 2x5, C is 4x2, and D is 3x1, then the dimensions of E= DACB are: О 3х1 O 1x2…

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Q: Show that if A is singular and Ax = b, b = 0, has one solution, then it has infinitely many.

A: Given: A is singular and Ax = b, b = 0

Q: If a, b, c are in GP and the equation ax² +2bx+c= 0 and dx² +2ex+f=0 have a common root, then is it…

A: Given that a,b,c in G.P and the equation ax2+2bx+c=0 and dx2+2ex+f=0 have a common root.

Q: 7.For which value of k will the roots of 2x + kox+1 = 0 be real? .2 1) 1 2) 2 3) 3

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Q: Use Gauss Elimination to solve the following set of linear eq's: 2x1 -6x2+x3=40 Зx2-13x3-50 4x1 +…

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Q: The set of solutions to z^6=−i is?

A: We have to find The set of solutions to z^6=−i.

Q: If one of the roots of ax^2 + bx + c is 2/3 + 5/9i where a, b and c are integers, what is the value…

A: Explanation of the answer is as follows

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

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Q: Given that the equation z2 + (p + iq)z + r + is = 0, where p, q, r, s are real and non-zero has a…

A: Introduction :--