A. Find the discriminant of each of the following equations and state what kind of roots the equation has. 1. 2r - 3x + 1 = 0 2. 4x + 5x – 7 = 0

Q: Find all the roots of the following equations. (a) z2 – 6z + 13 = 0. | (b) 2° – z = 0.

A: We will use basic knowledge of complex variables and mathematical logic to answer both parts of this…

Q: Find the roots of each of the following quadratic equations. 1. x^2 - 12x + 20 = 0 2. 3x^2 +…

A: We have to find the roots of the equations.

Q: Consider the following linear equation in fractional form: 5x x +1 + 4 4x – 1 %3D 2 Find the…

A: From the given problem: x+1+5x4=4x-12

Q: Find all the solutions of the Diophantine equation 30x + 12y = 6. %3D

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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: Determine the nature of the roots of the following equations: (a) 3x + 5x + 4 = 0 (c) x-8x + 16 = 0…

A: Since you have asked multiple subparts, we will solve the first three question for you. . If you…

Q: Which of the following is the standard equation of 9y² – x² + 2x+ 54y+62

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Q: Solve for y. (y+3) = 2y+y-5 If there is more than one solution, separate them with commas. 0..

A: Please refer the attached image for complete solution.

Q: Solve the following quadratic equation using any method to 1. x2- 10x + 25 6. 2x2 - x = 4 2. 2x2 +…

A: The quadratic equations are1. x2-10x+25=02. 2x2+5x-3=03. y2+4y=32 Note:   multiple questions are…

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: Which of the following are the approximate solutions of the quadratic equation 3x + 20x + 32 = 0? O…

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Q: Which of the following equations is a quadratic equation? O 2x° = (2x2 – 1) (3x + 4) %3D O 14x (x…

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Q: Solve the following vyrtems of equationr using matricer. a. 2x ty fz=4 -3xtay-22=-10 b. xt 3ytz= 10…

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Q: Determine the nature of the roots of the following equations: (a) 3x + 5x + 4 = 0 (c) x-8x + 16 = 0…

A: For a quadratic equation in the standard form  ax2+bx+c=0. first calculate the determinant D =…

Q: The given equation 4y – 2y2 +y – 3 = 0, how many - - complex roots are there? 3 O 2 01

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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: Solve the following equations y" - 4y + 4y = 8x² + 4x y" - 2y - 3y = sin 2x

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Q: 5. Find the æ-intercept(s) of the following quadratic equation. y = 9x? – 36x + 36 O x = 2 x = 6 x =…

A: To find the x- intercept put y=0 and Solve for x

Q: Which of the following quadratic equations will obtain 2 rational roots? A. 2x2 +11x + 12 = 0 B. 4x2…

A: To find which of the following quadratic equations will obtain 2 rational roots

Q: Determine the nature of the roots of the following equations: (a) 3x +5x + 4 = 0 (c) x-8x+ 16 = 0…

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

Q: Q1:- Solve the following Des 4) y" – 4y' + 3y = 4x+3e" 2x

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Q: Which of the following Diophantine equations can be solved? (a)12x + 14y = 31 (b) 16x + 7y = 17 89x+…

A: Diophantine equation equates to a constant the sum of two or more  monomials, each of degree  one.…

Q: Which of the following quadratic equations matches the given graph below? O y= 2x -4x+5 O y= 2x*…

A: Let the general form of quadratic equation y = ax2 + bx + c It has minimum value at x = (-b/2a) and…

Q: Determine the general solution of each of the following equations: (a) y" + 2y' + 5y = 3sin2x

A: a) Given:         y''+2y'+5y=3sin2x         5yx+2ddxyx+d2dx2yx=3sin2x This differential equation has…

Q: If the roots of the equation a(b – c)x² + b(c – a)x + c (a – b)=0 2 1.1 are equal, show that b а с a

A: Here we will show that 2b=1a+1c

Q: 2. t C .) x-L +さ-2= 2 2- %3D

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Q: (1+x²)y" + 10xy' + 20y = 0

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Q: 2x³y' = y(y2 + 3x²)

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Q: Find an equation whose roots are the 3 times the reciprocal of the roots of 6x-4x +3x-4 0. 6y' -4y?…

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Q: y" + 6y' + 8y = 3e-2# + 2x

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Q: Solve the following systerm: 2x + y-3z -3 x + 3y- 4z 11 x + 8y-9z 5 O(1, 2, 0) O (2, -1, 0) no…

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Q: Find all solutions to the following equation and plot each set of roots on an Argand diagram: z6 –…

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Q: Which of the following quadratic equations matches the given graph below? O y=6x+1 O y=6x+x O y=+1 O…

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Q: ind the x and y-intercepts of the equations x^2-2xy+4x=1 and  9x^2-4y^2=36

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Q: Find a particular equation for the DE: y+4y'-2y= 2x -3x+6

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Q: Find the Solution of the following Diffcrentíal Equations 26) 5-4y+3y=o y(0)=3

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Q: Find an equation for each line in the form ax + by = c, where a, b, and c are integers with no…

A: It is given that the given line is passing through the point 0,5 and it is perpendicular to the line…

Q: Let c, d e R and c > 2 + d. Show that the following equation has two distinct real solutions: x + cx…

A: Consider a quadratic equation αx2+βx+γ=0 So the roots of the above quadratic equation are given by:…

Q: If the roots of the equation a(b-c)x² + b(c-a)x+ c(a - b) = 0 - are equal, show that 2/b = 1/a +…

A: What is Discriminent: The discriminant of a higher degree equation in one variable determines the…

Q: Identify the "b" value of the following quadratic equation given below. 6 = (x- 1)2 O 5 O 1 O -5 -2

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Q: 1. Determine the characteristic of the roots of the quadratic equations. a) х? — х —30 %3D0 b) 7x –…

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Q: For each of the following quadratic equations, determine the number and the nature of the roots by…

A: If quadratic equation is ax2+bx+c then quadratic discriminant is b2-4ac If b2-4ac =0 then quadratic…

Q: 1. a) Identify the following equations as linear, quadratic or neither. i) y = -x? - 4x + 2 ii) y =…

A: We are authorized to answer three subparts at a time, since you have not mentioned which part you…

Q: 1, Without solving, find the sum and product of the roots of each of the following equations. 1.…

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Q: 2x³y' %3D у(у? + Зx?)

A: Rearranging the given differential equation we get,…

Q: OShow that every cubic equation of the form x³ + bx2 + c = 0 where b and c are real numbers has at…

A: Given: x3+bx2+c=0, where b and c are real numbers. The objective is to show that every cubic…

Q: #3. The following equations are quadratic in form. Rewrite each equation in the form au? + bu + c =…

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Q: Which of the following quadratic equations has the sum of product of the roots to be 4 and 7,…

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Q: Which of the following quadratics has imaginary roots? (1) x² +3x – 5 = 0 (3) 2x² – 3x+1=0 (2) x²…

A: For a quadratic equation: ax2+bx+c=0, the discriminant is calculated using the formula: D=b2-4ac.…