23. Explain why the equation x³ + x +1 = 0 has no real roots and why each of its complex roots is constructible.

Q: Find all complex solutions using an appropriate method. 18. (2x-3)(x+7)=1+11x-x²

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Q: Noah and Lin are each trying to solve the equation x^2-6x+10=0. They know that the solutions to…

A: Given data: The given expression for the polynomial equation is x2-6x+10=0. The given expression can…

Q: What are the roots of the equation x2 + 2x + 37 = 0 in simplest a + bi form?

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Q: Compute the discriminant of 4x2 - 8x + 1 = 0. What does the discriminantindicate about the number…

A: The discriminant of 4x2 - 8x + 1 = 0 is:

Q: Does the equation 4x2 + 20x + 25 = 0 have (a) two nonreal complex solutions, (b) two equal real…

A: 4x2+20x+25=0Formula: Discriminant, D=b2-4ac

Q: What are the roots of the equation 4x² + 10 = 11x in simplest a + bi form? %3D

A: Given,          4x2+10=11x

Q: Solve x2 + 2x + 2 = 0 in the complex number system.

A: Explanation: Given that,  x2+2x+2=0   Concept Used: Quadratic formula- x=-b±b2-4ac2a

Q: What are the complex solutions for z2- 2 +5 = 0? 士

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Q: What are the roots of the equation x2 - 16x + 65 = 0 in simplest a + bi form?

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Q: What are the complex solutions to the following equation: 0.5x2-0.2x +0.2 0

A: Given equation is 0.5x2-0.2x+0.2=0find out the complex solution of the given equation

Q: Select all the complex solutions for 2x² + 3x+ 9 = 0.

A: The equation is 2x2+3x+9=0. The quadratic formula for ax2+bx+c=0 is x=-b±b2-4ac2a. Here, a=2, b=3,…

Q: 4. Form the equation whose roots are the multiplicative inverses of the roots of 3x2 + 10x – 8 = 0.

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Q: Obtain all four roots of the equation = ++-0, and then express * +4 as product of quadratic factors…

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Q: Find all real and complex solutions of the equation 2x^2 +4x + 3 = 0.

A: Given: The equation, 2x2+4x+3=0.

Q: JUU A 10 3,735 - 3,60O = 135 tan 135° %3D 14) A student attempting to solve this Quadratic Equation:…

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Q: What are the roots of the equation x2 + 14x + 50 = 0 in simplest a + bi form?

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Q: find all complex Solutions for.each equation by handa X+3 18

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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: Find the complex solutions of the equation 2x + 2x + 3 = 0 using th quadratic formula. -1 tiV5 -1…

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Q: What are the roots of the equation 16x - 64x + 65 = 0 in simplest a + bi form? %3D

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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: What are the roots of the equation x² + 14x + 50 = 0 in simplest a + bi form? %3D

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Q: What are the roots of the equation 4x² = 8x – 9 in simplest a + bi form? -

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Q: What are the roots of the equation 25x +90x + 82= 0 in simplest a + bi form?

A: If equation is ax2 + b x + c = 0 then solution is  x = -b±b2-4ac2a

Q: What are the roots of the equation 5x+ 15 = 17x in simplest a + bi form?

A: Given equation is 5x2-17x+15.

Q: 4. Determine the roots of the equation x + 2x - 15. x + 2x = 15

A: Here, to determine the roots of the equation: x2+2x=15...(1)

Q: 2. Find all complex solutions: x2 +x+ 2 = 0

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Q: Compute the discriminant of 4x2 - 8x + 1 = 0. What does the discriminant indicate about the number…

A: Given: 4x2-8x+1=0

Q: Show that the equation 6x4 – 7x +1 = 0 does not have more than two distinct real roots.

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Q: That are the roots of the equation 4x2 8x – 7 in simplest a + bi form? %3D -

A: Explanation and solutions is given below....

Q: In the complex number system, x2 + y2 (the sum of two squares) can be factored as (x + yi)(x -…

A: To prove: x2+y2=x+yix-yi We know that a+ba-b=a2-b2 And we know that i2=-1 Solving the right hand…

Q: What are the complex solutions to the following equation? 3x2 – 2x + 3 = 0 -

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Q: What are the roots of the equation x2 – 10x + 26 = 0 in simplest a + bi form?

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Q: 1. Solve for x: 2x - 4x +7= 0. Write any complex solutions in terms of i and simplify any square…

A: The given equation is 2x2-4x+7=0. Calculate the complex solutions in terms of i and simplify any…

Q: For #3-4, solve the quadratic equation over the complex numbers. 3. x2 - 17x = 11 4. (x + 3)2 + 3 =…

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Q: Show that the equation r1 + x³ + 4x – 2 = 0 has exactly one real root.

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Q: 1. What are the roots of the equation (x + 1)(4x – 3) = 0? C) x= 1, - D) x= 1 A) x = -1,3 B) x= -1,

A: (x+1)(4x-3)=0⇒(x+1)=0 or (4x-3)=0⇒x=-1 or 4x=3⇒x=-1 or x=34⇒x=-1 ,34

Q: Show that the equation 5x* = 7x+5 has at most two real roots. %3D

A: To show that the equation 5x4=7x+5 has at most two real roots

Q: What are the roots of the equation x2 – 2x + 17 = 0 in simplest a + bi form?

A: We know that roots of the quadratic equation ax2+bx+c=0 is given by x=-b±b2-4ac2a Now, the given…

Q: What are the roots of the equation x2 + 18x + 97 = 0 in simplest a + bi form?

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Q: What are the complex solutions to the following equation: 0.5x2 0.2x + 0.2 =0

A: multiply both sides by 10 compare this equation with  so we have

Q: what is the roots of x2 _ 5x _ 2 =0 ?

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Q: 4. Construct an equation whose roots are less than 4 of the roots of x+3x-12x-10=0

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Q: If the discriminant of a quadratic equation is greater than zero, the roots of the equation are:…

A: The polynomial equation whose highest degree is two is called a quadratic equation. The discriminant…

Q: how was the roots of zeros found for this problem?

A: The zeros/roots of a function are the values of x-coordinates of the points, where the curve: y=f(x)…

Q: Find all complex solutions x4-3x2=28

A: Given equation

Q: Use Descartes’ rule of signs to determine the number of possible positive, negative, and nonreal…

A: Given equation              x5+4x4+3x3-4x+2=0

Q: 2. Isabel believes that f(x) = x3 - 9x2 + 27x - 27 has 3 complex roots. Nicky told her that it has 4…

A: Here we will use some basic results.