Project

Quadratic Solver

CSc 1350: Programming Project # 2

Solving Quadratic Equations

Out: 9/21

Due: 10/6 by 11:50 PM

Learning Objectives

• Using Conditional Statements,

• Using Logical Operators,

• Using Standard Math Class methods,

• Using Basic Arithmetic Operators, and

• More on Writing Interactive Programs

Definition 1. A Quadratic Equation is a second-order polynomial equation in a single variable x.

ax2 + bx + c = 0

(1)

with a = 0. a is referred to as the coefficient of the quadratic term, b, the

coefficient of the linear term, and c, the constant term. Because a quadratic

equation is a second-order polynomial equation, the fundamental theorem of

algebra guarantees that it has two solutions. These solutions may be both

real, or both complex.

Definition 2. The quantity D = b2 − 4ac is called the discriminant of a

quadratic equation.

Since we have covered decision statements, we will consider quadratic equations whose roots are real or complex numbers.

Duncan

1

Fall 2015

Quadratic Solver

CSc 1350: Programming Project # 2

For any quadratic equation, its roots may fall into one of these categories:

1. The discriminant, D, is 0:

x=

−b

2a

2. The discriminant, D, is positive:

x=

√

√

−b + D −b − D

,

2a

2a

3. The discriminant, D, is negative:

x=

−b

+

2a

|D| −b

i,

−

2a

2a

|D|

i

2a

where, i is a symbol representing the imaginary number.

Observe that when the discriminant is a negative number, the roots of the

quadratic equation are complex numbers. When the discriminant is 0, the

roots of the quadratic equation are identical and real. When the discriminant

is a positive number, the roots of the quadratic equation are distinct real

numbers.

Write a Java program that prompts the user for the coefficient of the

quadratic term, the coefficient of the linear term, and the constant term of a

quadratic equation. If the coefficient of the quadratic term is 0, your program

prints a message...