Given the roots are: z 8 ± 2i, write the quadratic equation, by correctly filling in the blanks. First, plugging into the formula: y = =-2( x+ Then, the simplified equation is: y = r2-

Q: B. Find all roots of (2i)2

A: for finding roots note 2 point a² + b² + 2ab = (a+b)² i² = -1

Q: Given that a, B and y are the roots of the equation 423 – 522 + 3z + 11 = 0. a3 Without finding a, B…

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Q: Solve the following equation for b. 1 A= b°c b = (Type an exact answer, using radicals as needed.…

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Q: Solve the following equations for the real numbers, x and y. a. (3 + 4i)2 - 2(x - iy) = x + iy

A: We simplify the given equation

Q: I. Solve using De Moivre's Theorem. Find the 2 square roots of 3 – 8i

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Q: Solve the following auxiliary equations by factorisation (if possible) -6+ v6? – 4ac OR by using the…

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Q: 1.) 6x² + Ilx - 35 = 0 |3| 2) 20x² – 15x -10 = 0 3) 2x2 +8X =0 4) 4x2 +3x - 2=D0 5) 2x2- 64=0

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Q: Solve, for z, the equation lnz = 4 – 3i.

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Q: A flare is launched from a life raft with an initial upward velocity of 192 m/s. a) How many seconds…

A: Given h(t) = 192t -16t2   a. After returning to sea h= 0 192t -16t2 = 0 t (192-16t) = 0

Q: Solve the equation using Lagrange's method: 2x² –15x+18=0 |

A: Given the quadratic eequation:      2x2-15x+18=0 Solve it using Lagrange's method.

Q: a. x² +8x-3 = 0 Find the equation with following roots: -4+2i6

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Q: If r; and r, are the roots of equation x² – 2x+4 =0, then find Er .

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Q: Use De moivre 's theorem to find roots of given equation and also sketch the roots on the Argand…

A: Given : x3=1+i We know that polar form of z=x+iy is defined as z=rcosθ+2kπ+isinθ+2kπ, where r=z and…

Q: If pq > 0 and the roots of (x' + mx + m = 0 are in the ratio p:q then equals (a) 1 (b) 0 (c) (d)

A: We know, lx2+mx+m = 0Let,p, q be the roots of the quadratic equationwe know that,1. p+q = -ml2. pq =…

Q: refer to the given: (D* + 6D: + 9)y = 0 Solve for the roots: +/- V2i , +/- VZi +/- V4i , +/- V4i A.…

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Q: Find the real solution(s) of the given equation. 36x4 + 16 52a? Give exact answers using fractions…

A: Given,36 x4+16 = 52x236x4-52x2+16 = 0Let,x2 = a36a2-52a+16=0

Q: Let ne Z and AABC be a right triangle with right angle at C. If sin A and sin B are the roots of the…

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Q: show that 1+i is a root of the cubic equation 3z^3-5z^2+27z-45=0, find the other two roots

A: 3z3-5z2+27z-45 = 0Using rational root test :±11, ±13, ±31, ±51, ±91, ±93, ±151, ±153, ±451,…

Q: It is given that a and B are the roots of the quadratic equation 2x+4x- 3 = 0. Form a quadratic…

A: If α and β are the roots of the quadratic equation ax2+bx+c=0, then α+β=-baαβ=ca Consider the…

Q: The roots of the equation x + x(p – q) – (q – r)(p – q) = 0 are ?

A: In this question we have to find roots of the equation.

Q: The product of the roots of equation 3x +9x-12=0 is إختر أحد الخيارات: -4 .a O .b O None of these cO…

A: Equation : 3x2 + 9x - 12 =0

Q: B- Find the root of the following equation (use Newton- Raphson method): 2x3 – 7x – 2 = 0

A: given equation is   2  x 3-7x-2=0   let f(x) = 2x³-7x-2=0 => f(x)=6x²-7   we have to find…

Q: AD bisects LA. Solve for DC By Thearem, A 30 24 B

A: In the given triangle ABC, AD bisects ∠A. we have to DC

Q: y" – y = sin? x Using the method of indeterminate coefficients, solve the particular solution of…

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Q: Use the Newton-Raphson method of finding roots of equations to solve the following: where a = 2.5. 1…

A: The Newton-Raphson method (also known as Newton's method) is a way to quickly find a good…

Q: Q.4. Use Lagrange's formula to solve a quadratic equation: 5x-8x+3=0

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Q: For what values of the parameter a does the equation x + 2ax³ + x² + 2ax+1=0 have at least two…

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Q: z₁ and z₂ are the roots of 32² + 3z + b = 0. If O(0), (z₁), (Z2, form an equilateral triangle, then…

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Q: re cube roots of unity, tl w?) is

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Q: iz² + 18i = 40

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Q: Find real numbers a and b such that equation is true.  a+bi=7+2i a= b=

A: Here we need to use equality of two complex Numbers  Real parts are equal  and imaginary parts also…

Q: Reduce to first order and solve, showing each step in detail. 2xy" = 3y'

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Q: Now, using the general form of solution as shown above, with a and B, find the exact solution that…

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Q: Solve for b when c = 32 mm, and a = 18 mm.  Round the answer to 2 decimal places.

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Q: Find the imaginary part of 23t where z = x+ iy (the denominator is the conjugate

A: The conjugate of z will be x-iy

Q: The equation z + pz+q = 0 is given. Find parameters p and q such that the difference of roots of the…

A: Given :          x2 + px + q = 0 To find:           the value of p and q Let a and b be two roots .…

Q: Express the complex solutions of the equation z^n + 1 = 0, where n ∈ N, in  terms of roots of unity.

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Q: Identify all three (distinct) solutions to the equation z3 = 27i. Write your answer in x + iy form.

A: Given equation is z3=27i we have to find the solution in x+iy form

Q: Solve the following quadratic equation by using the quadratic formula. If needed, submit your answer…

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Q: Q1/ Find the cubic root of Z = -i?

A: As per our guideline we are allowed to do 1 question at a time. Please post other questions next…

Q: List the solutions of the equation: 0 = 4.x 12x + 18 Your answers must be in exact form, do not give…

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Q: Given the equation y = z² – 2z + 1, determine how many roots there will be.

A: Roots of a equation are the values of x for which f(x)=0.

Q: Q 8. 2 A

A: Triangle Question

Q: By the Lagrange's method, the roots of the equation 2x-7x+6=0are: x=- (tu -a) 7. here a =--. Then…

A: Option (b)  1/2 is correct.

Q: Let n = Z and AABC be a right triangle with right angle at C. If sin A and sin B are the roots of…

A: What is Quadratic Equation: When a quadratic polynomial assumes the value zero, that equation is…

Q: . Given that z = 1 is a root, find the other two roots of 2z3 −z2 +3z−4=0

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Q: Find all root s 니 2.V-니

A: Given : 2 × -44

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.