Find the quadratic equation with real coefficients that has the complex number z = 8-7i as...
1(a) Find the square roots of the complex number z -3 + j4, expressing your answer in the form a + jb. Hence find the roots for the quadratic equation: x2-x(1- 0 giving your answer in the form p+ q where p is a real number and q is a complex number. I7 marks] (b) Express: 3 + in the form ω-reje (r> 0, 0 which o is real and positive. θ < 2π). Hence find the smallest value of...
1. Write a quadratic equation that has integer coefficients and has as solutions the given pair of numbers. (Use x as the variable.) and 5 _____?______ 2. Evaluate for the given values of a, b, and c. Write the result as a complex number. a = ?4, b = 2, c = ?5 _____?_______ 2
NAME: Q1. (30pts) Solve the quadratic equation 22- (8+ i)z + 17+ i = 0 by realizing the following plan: (i) find the discriminant A of the equation: (i) write a program for a scientific calculator to obtain the polar form r(cos+ i sin ) of A and the 'first' root ( cos isin 2 of degree two of A; (ii) execute the program, fix the results, find another root A of A of degree two (before executing the program,...
java code Design a class named QuadraticEquation for a quadratic equation with real coefficients ax? + bx + x = 0 where a = 0. The class contains: (a) Private data fields a, b, and c that represent three coefficients. (b) A constructor taking arguments for a, b, and c. (c) Getter and setter methods for each attribute field. (d) A method named getDiscriminant() that returns the discriminant, 62 - 4ac. (e) A method named hasReal Solution that determines If...
This is in python language Algebra: solve quadratic equations) The two roots of a quadratic equation, for example, 0, can be obtained using the following fomula: b 4ac is called the discriminant of the quadratic equation. If it is positive, the equation has two real roots. If it is zero, the equation has one root. If it is negative, the equation has no real roots. Write a program that prompts the user to enter values for a, b, and cand...
Find the real part of the complex number a + bi obtained as the square root of -2.4 +4.1i, where 0° <e < 180º.
Find all solutions (real or complex) to the following: (a) z² + 2+2 = 0 (Suggestion: quadratic formula) (b) z4 – 16 = 0 (Suggestion: factor -- difference of squares)
I. (a) Find the general complex solution for the following homogeneous equation: y"-y" + 81/ + 10y = 0. (One root of the characteristic polynomial is λ| =-1.) Your solution must have three (complex) integration constants. (b) Because the coefficients of the equation are real, it makes sense to ask what is the most general real solution. Obtain it by separating the real part of the solution you found in (a). Your result must have three real integration constants 2....
quadratic equation by PHP The purpose of this question is to develop a simple calculator for solving a quadratic equation of the form . The solution of the quadratic equation can be classified as a real or an imaginary solution. In this question you are required to apply two formulas for solving the quadratic equation; the discriminant formula and quadratic formula. The discriminant formula is applied for determining whether the quadratic equation has a real or imaginary solution, where the...
The roots of the quadratic equation ax2 + bx + c = 0, a following formula: 0 are given by the In this formula, the term i2 - 4ac is called the discriminant. If b4ac 0 then the equation has a single (repeated) root. If -4ac > 0, th equation complex roots. Write a program that prompts the user to input the value of a (the coefficient of ), b (the coefficient of x), and c (the n has two...