Derive the quadratic formula for the zeros of ax2+ bx + c, where a, b, and c are complex numbers and a ≠ 0.

Q: 2. Write down the complex (a) 3+ j4, (b) 2 j. [(a) 3 -

A: See the details solution in below

Q: Show that in general , the sum of the roots of a quadratic equation ax2 + bc +c =0 is - b/a whereas…

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

A: Given equation is  x^7 -1=0

Q: Solve the complex equation (2+j)(3-j2)=a+jb

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Q: Find all complex number solutions to the equation. x3 - 512 = 0

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Q: Use the guadratic formula to solve for x. 2x-6x-1=0 (If there is more than one solution, separate…

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Q: Find all complex solutions of 2x +3x+6= 0. (If there is more than one solution, separate them with…

A: use quadratic formula for finding complex solution.

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

A: Given : fx = x2+2x+2

Q: Let x₁, x₂ are the roots of the quadratic equation x² + ax + b = 0, where a, b are complex numbers…

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Q: Exercises 35 and 36: Find all complex solutions. 35. 4x + 9 = 0 36. 2x2 + 3 = 2x

A: Given: 4x2+9=0 For finding solutions of given equation, we simplify it

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: Exercise 6.4.1 Show that 1 +i,2+i are the only two roots to P(x) =x² – (3+2i).x+(1+3i) Hence complex…

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Q: Solve by using the quadratic formula: x +10x+9 =0 O A. 5+4i and 5-4i O B. -5+4i and -5-4i O C. 4+5i…

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Q: Use the discriminant to determine the number of solutions to the quadratic equation 12q^2+10q+4=0…

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Q: Use the discriminant to determine whether the quadratic equation below has one real number solution,…

A: A polynomial equation whose degree is 2, is known as quadratic equation. A quadratic equation in its…

Q: Solve by using the quadratic formula: x +10x+16=0 O A. 5+3i and 5-3i B. -5+3i and -5-3i O C. 3+5i…

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Q: Assume that P and Q are two positive distinct real roots of the quadratic equation (²₂. - -…

A: given quadratic equation t2-P+Qt+PQ=0 here assume that P and Q are two positive distinct roots of…

Q: In the complex number system, find the complex solutions of theequation x2 + 2x + 2 = 0.

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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: Find all complex solutions of 6x2 – 5x+4 = 0. (If there is more than one solution, separate them…

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Q: Which of the following representations of a quadratic has complex roots? Oal 9x2 + 33 = 0 b) -2.5 -2…

A: Hello! Thank you for the question but as per our honor code, we'll able to solve only three subparts…

Q: 10. Which of the following quadratic equations has the complex number 2-i as a solution? 22 +2 0 B 2…

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Q: 29. Use the quadratic formula to find the roots of the following quadratic: y = 2x² – 11x + 5 -

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Q: Find all real and complex solutions to the equation   x^3 − 3x^2 − 10x + 24 =0

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Q: Which of the following representation of a quadratic has a complex roots?

A: The given quadratic equation is: 9x2+33=0 To find its root simplify the given equation 9x2+33=0.…

Q: Let x₁, x₂ are the roots of the quadratic equation x² + a where a, b are complex numbers and y₁, y2…

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Q: Find the fourth roots of 2 + v2 i, namely all complex numbers z such that z* = v2 + V2 i

A: The representation of a complex number can be done in two forms, rectangular and polar forms. The…

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

A: Given that

Q: 6. Show that the quadratic equation ax² + b – a = 0 (a± 0) has two distinct real roots.

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Q: Show that root of following quadratic equation are complex numbers a. 2x2 + x + 3 = 0 b. 7x2 + 5x +…

A: Compare the equation 2x2+x+3=0 with the general form of the quadratic equation ax2+bx+c=0, to find…

Q: use the discriminant to help solve each problem. Determine k so that the solutions of x2 - 2x + k =…

A: Given equation: x2-2x+k=0 If descriminat D=b2-4ac<0 is negative, the equation has no real root…

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: 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: Write a quadratic equation with roots of 1 / 6 and 5 / 8 in the form ax2 + bx + c = 0 , where a,b,…

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Q: Find all the roots of the equation (3z-1)^4+(z-2)^4=0 in the simplified form a+ib

A: Given equation, (3z-1)4+(z-2)4=0 Expand this equation,…

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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: 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: Which of the following representations of a quadratic has complex roots? Oal 9z2 + 33 = 0 y -2.5 -2…

A: For finding which quadratic equation have complex, we find roots of all equation given in options…

Q: Find all complex solutions of 2x + 3x+ 6 = 0. (If there is more than one solution, separate them…

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

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Q: Find the roots of the equation z³ +2 – 2/3i = 0. %3| -

A: Given: z3+2-23i=0 So,  z3=-2+23iz3=2-1+3iz3=4-12+32i We know that z=rcosθ+isinθ=x+iy, where r=x2+y2,…

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: Write a quadratic equation with integer coefficients that has the given roots. x = 2 – 3i, x = 2 +…

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Q: 2. Write an equation in standard form ax? + bx + c that has roots of x = 4,. %3D

A: The roots of given equation is x=4,12 To find the equation in standard form

Q: Find all complex number solutions to the equation x^y =y^x , where x and y are both nonzero.

A: We need to find all complex number solutions to the equation xy=yx, where x and y are both nonzero.…

Q: it is given that α and β are the roots of quadratic equation 2x^2-5x+6=0.Form a quadratic equation…

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Q: Find all complex solutions of x+5x+7=0. (If there is more than one solution, separate them with…

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

Roots

The main dissimilarity between real and complex roots is that the real roots are obtained as real numbers, in contrast with the complex roots, which are indicated as imaginary numbers. The standard format for depicting any complex number is in the form of a + bi.