Completely factor P(x)=x* +x + 4x+16x-192 into linear factors, given that -4i is a zero. P(x)= (Type your answer in factored form. Express complex numbers in terms of i.)

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

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Q: Find all complex solutions using an appropriate method. 21. x – 3x? – x+3=0

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Q: 16) Given the function f(x)=2x –1lx² +22x–15, find all the complex roots, given that 2-i is a root.…

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Q: Find all complex solutions of 3x+x+4%3D0. (If there is more than one solution, separate them with…

A: We have to find complex solutions of given equation.

Q: solve the complex equation using demoviers theorem x' – 1 = 0

A: Given equation is  x^7 -1=0

Q: Find all complex square roots of 3+3/3 i. In other words, find all complex solutions of x= 3+33 i. i…

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

A: Given: to determine the number of possible positive, negative, and nonreal complex solutions of the…

Q: What does Descartes’ Rule of Signs tell you about the real roots of x3 – x2 + 1 = 0 ?

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Q: State the number of complex zeros and the possible number of real and imaginary zeros for the…

A: Given : fx = 2x4-9x2-5

Q: 2. Find all complex solutions of 6x-5x+4 0. (If there is more than one solution, separate them with…

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Q: In the complex number system, find the complex zeros off(x) = x2 + 2x + 2

A: Given : fx = x2+2x+2

Q: Completely factor P(x)=x" +2x'+ 8x + 32x- 128 into linear factors, given that - 4i is a zero. P(x) =…

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Q: Two complex solutions of the form a ± bi of a polynomial equation with real coefficients are________…

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Q: L0. Factor f(x) = x +2x+9x+ 18 completely into linear factors, include complex factors as well as…

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Q: P(x) = 3x – 4x3 + 2x² + 3x – 6 How many complex zeros does the above polynomial have?

A: We have to find the complex roots

Q: Find all complex square roots of 1+V3 i. In other words, find all complex solutions of x=1+/3 i.

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Q: What is the complex conjugate of -6 + 4i?

A: Complex number is -6+4ithen complex conjugate is -6-4i

Q: According to the Fundamental Theorem of Algebra, the graph of fx) = -x2 - 2x +1, ha v two complex…

A: According to question We have to calculate the number of complex roots using fundamental theorem of…

Q: EXAMPLE 5 Using Square Roots of Negative Numbers Evaluate (V12 – V-3)(3 + V-4), and express the…

A: The given expression is, 12--33+-4 On simplifying the terms, we get…

Q: Find the complex conjugate z, of z1 = -4i + 4. ž =

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Q: Q3) Find complex root of the z³ = -27, k = 0,1

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Q: Express the complex number in exponential form. z=4-6i

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Q: 3. Find the complex zeros of f(x) = x – 4x2 + 25x 100.

A: fx=x3-4x2+25x-100=x3-4x2+25x-100=25x-4+x2x-4=x-4x2+25=x-4x+5i(x-5i)

Q: Given that Z1 and Z2 are complex numbers, show geometrically or otherwise that |Z1| - |Z2| is less…

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Q: 3. a) If 2 - i is a root of x3 – 2x² – 3x + 10 = 0, find the other complex root. b) Calculate the…

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Q: 1. Determine the real zero, and a complex conjugate pair of zeros for the equation below. 5x* – 16x³…

A: Given:      5x4 -16 x3 + 57 x2 + 120 x + 120

Q: State the number of complex zeros and the possible number of real and imaginary zeros for the…

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Q: Find the value of x in the complex equation (2x - 3yi)(3 + 4i) = 78 - 21i %3D

A: Given complex equation (2x-3yi)(3+4i)=78-21i To determine the value of x  First multiple left hand…

Q: Find all complex solutions to x3 +1=0

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Q: Find the value of y in the complex equation (2x-3yi(3 + 4i) 78-21i O5 -3 03 -4

A: Given, (2x-3yi)(3+4i)=78-21i Expanding the LHS⇒ (2x-3yi)(3+4i)=6x+8xi-9yi-12yi2…

Q: Find all the rational, irrational, complex zeros x^4+3x^3-3x^2-15x-10

A: Given information: x4+3x3-3x2-15x-10

Q: Find all complex solutions of 5x+5x+3=0. (If there is more than one solution, separate them with…

A: Given that: 5x2+5x+3=0

Q: Find all complex solutions of using the quadratic formula 2x^2-3x+5=0

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Q: Find all complex solutions using an appropriate method. 27. x

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Q: Derive the quadratic formula for the zeros of ax2+ bx + c, where a, b, and c are complex numbers and…

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Q: Show that the solution of the equation  4x2 + 24x + 37 = 0 are complex conjugates of each other.

A: Given quadratic equation: 4x2+24x+37=0

Q: Find all complex solutions of 3.x-2.r+ 1 = 0. %3D

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Q: Find all complex solutions of x-5x+7=D0. (If there is more than one solution, separate them with…

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Q: Find all solutions of the equation and express them in the form a + bi. 3x2 + 1 = 0

A: Consider the given equation as 3x2+1=0

Q: 8.3) Solve the equation z – 8 = 0, using De Moivre's theorem, giving the results as complex numbers.…

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Q: 10. What pair of factors should be used to find the complex solutions for x? 49x+36 0 (6x-71)(6x+ 7)…

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

Q: 6. Express the roots of the equation x + 1 = 8(x- 3) in a+ bi form.

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Q: Find all complex solutions of x- 6x+2=0. (If there is more than one solution, separate them with…

A: Given: x2-6x+2=0 Quadratic formula: The solution for the quadratic equation ax2+bx+c=0 is…

Q: P(x) = 3x^5 – 4x^3 + 2x² + 3x – 6 How many complex zeros does the above polynomial have?

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Q: Find all complex solutions of 6x (If there is more than one solution, separate them with commas.)…

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Q: Find all (complex) zeros of P(x)=x^4-5x^3+2x^2-10x

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Q: f(x)=-4x3+x2-9x+6 what is the possible number of nonreal complex zeros?

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Q: Prove that x^2 = 4 will result into ± 2 using complex numbers.

A: Given that, x2=4

Q: Find all complex fourth roots of 4. In other words, find all complex solutions of x* = 4.

A: Given,          Complex fourth roots of 4.