10-26 Exercise 3: Find roots of a quadratic equation

Question

14k views

Write a program to find roots of a quadratic equation

A quadratic equation is a second order equation having a single variable. Any quadratic equation can be represented as where a, b and c are constants ( a can't be 0) and x is unknown variable.

寫一個找二次方程的求根程式

For Example

is a quadratic equation where a, b and c are 2, 5 and 3 respectively.

To calculate the roots of quadratic equation we can use below formula. There are two solutions of a quadratic equation.

使用下列公式:

x = (-b + sqrt(D))/(2*a)
x = (-b - sqrt(D))/(2*a)

where, D = (b*b-4*a*c) is Discriminant (判別式), which differentiate the nature of the roots of quadratic equation.

For the complex result (複數根):

realPart = -b/(2*a);
imaginaryPart =sqrt(-D)/(2*a);

Note: We have used sqrt() function to find square root which is in math.h library.

Example input 1:

1 2 1

Example output 1:

Roots of 1.00x^2 + 2.00x + 1.00 = 0 are real and same
x1 = x2 = -1.00

Example input 2:

1 -3 2

Example output 2:

Roots of 1.00x^2 + -3.00x + 2.00 = 0 are real and different
x1 = 2.00
x2 = 1.00

Example input 3:

1 2 2

Example output 3:

Roots of 1.00x^2 + 2.00x + 2.00 = 0 are complex and different
x1 = -1.00+1.00i
x2 = -1.00-1.00i

[Exercise] Coding (C) - asked Oct 26, 2017 in Chapter 5: Selection Statements by semicolon (5.2k points)
ID: 28934 - Available when: 2017-10-26 18:00 - Due to: Unlimited
reopened Oct 26, 2017 by thopd | 14k views

56 Answers

Page:

« prev
1
2
3
4
5
6
next »

112233 · Answer 1 · 2017-11-09 17:27:38

Hidden content!
#include ****** *** * **
#include   **** * * ** 

int main()
{
*** ** * * *** ** **  ***** a, b, c, determinant, x1,x2, realPart, **   * *


   **  **  *   *** * ****   * * * ** %lf  **  ** **  ** *** &b, &c);


  *** *** ***  **  ***  ****   *   = b*b-4*a*c;

* ****  *** **      *         condition for real and different roots


       * * *    **  *  ***  *  * ** for real and equal roots
  *  **    * * * * **   *    (determinant == 0)
 *  ** **  *    ********
* *  ***        ***   *** * ** * *       *       ****  = x2 = -b/(2*a);
**   ***** *** * *  * * ** *** *** **  ****** * ***     *** * **  ** * * of %.2fx^2 + %.2fx + %.2f = 0 are real and  *   ***** a,b,c);
** *   ***  *  * *  **     * *** * **  *   ** ***  * *   **    = x2 =    **   * x1);
 **  ****** *** **   * **  *  *   

  **  ** ** *** *** * ***  **      if   *****  > 0)
     ***     *  **    *** ** *
*  * *****       **  *  *** * **  * sqrt() function returns square root
    *** *** **  *****  ***       * * *****    ** *** ***  = ** **     *  **   **
**** ** * *    * **** * *  ***   *   *** **  *      =  * * *  * ******

    ** * **   *      ****** *     *   * * *  * **   ** *  ***  ***    *  of %.2fx^2 + %.2fx + %.2f = 0 are real and  **    ** **   * 
* **    **  * ** **  ****** * * *  ***** ****   ****   * *   *  * =     ** * * x1);
 * *    ** * * *** **  *** ***** *      *  *** *  ** **   =  ***** ****** x2);
* ** *  *     ** ****  ***  if roots are not real
**** * *** *  *  * *****  *** 
 * *    *  **    *   **
* * * *  **    *   **** *  *  * * *   * ***      ***   ** *** *  = -b/(2*a);
*** *  * * **  **** **    *   *   *  *   * **    ** *  *   * =  * ** ** * * ****
*** *    *** **  * **** ** *   **      * * ****     *  ***    ********   of %.2fx^2 + %.2fx + %.2f = 0 are complex and     ** * *  a,b,c);
***   *   **  ** * ******      **  ****   *** * *   *** *** =  ***** **** realPart, ***    ** * 
** * ***** *  *    *   * *** *  *   ** ***     *   * **  * * * = ******  *** realPart,  ***  * *
   *  ******* *****    ***

**  *   **** * ** ****    * * 0;
}

answered Nov 9, 2017 by 112233 (-167 points)

112233 · Answer 2 · 2017-11-09 17:17:35

Hidden content!
#include *  * ** ***  **  
#include  ***   * **    

int main()
{
**** * * * * * *** * **** **  *   * a, b, c, determinant, x1,x2, realPart, *  *  * *


  *** * ** ****** ** * **** * * *  * *  *   %lf  **  **  *** ****  * &b, &c);


 ** ** *     *   * *   ** * ***** ** *  ** = b*b-4*a*c;

*   * * *  *     * *     *   condition for real and different roots
* *      ** *  ** * * **  (determinant > 0)
* ** * *   * *   *   ** * *    
  *  **** *   ****   *        ** sqrt() function returns square root
*   **  ***  ******* * * *****    **   *  ****  *    * **  = *  ** ** **  * *  **   
  ***  *** ******   *     *  **** *    ****** * ** *  *  * = ** ****   **  ** * 

**   *******  * * * *****  *     * * **** **** * * * ** * of %.2fx^2 + %.2fx + %.2f = 0 are real and    **  * **  *  * *
** **** **  **    *   *  * *  * *      * * * * ***  ** ** ***   *  * *   =     **   x1);
** * **  *** * **   ** * *  **  ** *     ***  **** ** *  ***  ** *** = *** ** ** ** x2);
** *** **   **  *   **** ***

*  **  **** * **       * **  *****  *** for real and equal roots
 * **      ** *** ******* if (determinant == 0)
  *  ** ***  * *  * ****
* *  *   * * *  *** ** ***  **  ** * ***  ****  = x2 = -b/(2*a);
* ** ****   **  * * ****** *** **  * * *   * ****   **   ** **** of %.2fx^2 + %.2fx + %.2f = 0 are real and  * * * ** a,b,c);
      **** *** *** *  *  * **     ** * ** *   ** * * ** ***     *** = x2 =   * * **  ***  x1);
** * * * * *******  *    *

* * *** *  *  ****  **    if roots are not real
* ** * * *  ** * * *   * ** *  **
*  * *** *     ****   ****
**** **  *     ** ***** ** ** *   ** *  * *******   ***** *    * = -b/(2*a);
 * **** *** *  ** *      *** *****   * ****** * **** * **     =   ****    ******
 **  *   **     *  **** * **    * *  * **       * *   **  *   **   of %.2fx^2 + %.2fx + %.2f = 0 are complex and       ** *** * * a,b,c);
**    * *  *   ***** *  ***  *  *    *   *** *  * * ***     =  ****** ******* realPart,  **** * **
**  ****** * ** *  *   ** * ****  * * **  ** * *  *   **  *** * =   ***  **  * realPart, *  **  **
 **  ** *  *** *        *** * *  ***

* *  **** * * *  *  ** **** 0;
}

answered Nov 9, 2017 by 112233 (-167 points)

garrylin2 · Answer 3 · 2017-11-02 19:54:55

Hidden content!
  *   ***  ***  * **  
**  *  *  *   *     
int main(void)
{
* *** **   ******  * * ****** a,b,c,d;
 *****   * ** ***** *  * *  *   *  *   %f ** *** *     ** **    * ** 
**  * **  ****** *    ** *  ** *   *  
*   ** *       ** * *** ***   ***
 **  **  * *  * **** *   * ***  *    * **** ***  * * *      * of %.2fx^2 + %.2fx + %.2f = 0 are real and ***   ** = %.2f\nx2 =  ** *  **   *   +   *  ** **   -   ** * *   
*  *******   * *   ** *
 * ***      ***  *** * * * **   (d==0){
* **   *** * ** ******       * ** *** **   *   ***  *****  * * * *  of %.2fx^2 + %.2fx + %.2f = 0 are real and same\nx1 = x2 = ***    *** +  *   ****
     *******    * ****** *** 
 *** ** **   * ** * ***** *   *  (d<0) {
  ** *******    *   * * ** *** ***    **  *   *   ** ** ***         * **    of %.2fx^2 + %.2fx + %.2f = 0 are complex and ** *   = * *  *  *** = ***  ** ** **  ****  *  **  *   *    * *  ** * * * *   *
**  ***  *   *  **   *  ****
}

answered Nov 2, 2017 by garrylin2 (-204 points)

garrylin2 · Answer 4 · 2017-11-02 19:53:31

Hidden content!
* ** ** ** *   * *** 
**** ****** *   ***  ** *
int main(void)
{
   *** * *** **** *    **    * a,b,c,d;
  * * * * **   ***  *   *   **   *  ** *  * %f  * **  **   * *  *   *  * *   
*  **   * **  *** *    *  *
  *   ** *  *** * *** * ***  (d>0){
    *    * *    ** * **  *  ** *** * * * **** *  *  ** * * **   * * * *   * of %.2fx^2 + %.2fx + %.2f = 0 are real and   ** * = %.2f\nx2 = *    *  **  * *  * + * * ** *  -   * ***  
****   *   ** * * *** **
 *  * **** *****   *     (d==0){
***   *     *   * *  *     * * *** ***       *     *    ** *  of %.2fx^2 + %.2fx + %.2f = 0 are real and same\nx1 = x2 =  *  *    ***       +   * *  ** 
** ***  ** ***   *    * * *  
 *   ** ******     **    ** *  {
  ***   *** **** * *** * *    *******  **  *   **  **  * * *  ****  **     *** of %.2fx^2 + %.2fx + %.2f = 0 are complex and      *** = *     * * = * *  *  **** **    ** *** * *  * *    ***   ** * 
   ** ***  *  * * ** *  *** 
}

answered Nov 2, 2017 by garrylin2 (-204 points)

rick · Answer 5 · 2017-11-02 19:34:07

prog.c: In function 'main':
prog.c:5:5: warning: implicit declaration of function 'scanf' [-Wimplicit-function-declaration]
     scanf("%f %f %f",&a,&b,&c);
     ^~~~~
prog.c:5:5: warning: incompatible implicit declaration of built-in function 'scanf'
prog.c:5:5: note: include '<stdio.h>' or provide a declaration of 'scanf'
prog.c:13:9: warning: implicit declaration of function 'printf' [-Wimplicit-function-declaration]
         printf("Roots of %.2fx^2 + %.2fx + %.2f = 0 are real and different\nx1=%.2f\nx2=%.2f\n",a,b,c,x1,x2);
         ^~~~~~
prog.c:13:9: warning: incompatible implicit declaration of built-in function 'printf'
prog.c:13:9: note: include '<stdio.h>' or provide a declaration of 'printf'
prog.c:17:9: warning: incompatible implicit declaration of built-in function 'printf'
         printf("Roots of %.2fx^2 + %.2fx + %.2f = 0 are real and same\nx1 = x2 = %.2f",a,b,c,x1);
         ^~~~~~
prog.c:17:9: note: include '<stdio.h>' or provide a declaration of 'printf'
prog.c:21:9: warning: incompatible implicit declaration of built-in function 'printf'
         printf("Roots of %.2fx^2 + %.2fx + %.2f = 0 are complex and different\nx1 = %.2f+%.2fi\nx2 = %.2f-%.2fi",a,b,c,x3,x4,x3,x4);
         ^~~~~~
prog.c:21:9: note: include '<stdio.h>' or provide a declaration of 'printf'

rick · Answer 6 · 2017-11-02 19:28:09

Hidden content!
#include<stdio.h>
#include<math.h>
int main()
{
   * * *  *   *** *** *   *  ** a,b,c,d,x1,x2,x3,x4;
 *    * *  ****** *    * ***  ***  * *  %f *  *  **** * *** *   *      * 
** *    * ***  **    **   **    * 
  *  *** * *   *  * * *   *  * * **   * ***
* *  ** * * *   *    ***   * *****      *** 
  *    * *   **   ***  * *  * * *    *  ***
***   ******  *   * **  *   *  ** ***   
 **  ***  *    * *      * ** *   ** *  ** *  *  **  ** *  **
  * **    *     *** *   *   
 ** *  * *  ***    *   *  * *   **** ** * **** * *** *  ** *******  of %.2fx^2 + %.2fx + %.2f = 0 are real and ***** *  *  ** **     *** ** * **** 
 * **      *   * ***   ** * *  * *
 **** ** *** **  * ***   *  **   *  * * ***** ****  *   * *
 *  * **  *  ** * ****** *    *
  * *  **  *  **  *    *** ** * *** ** ** *     *  *** **** *****   of %.2fx^2 + %.2fx + %.2f = 0 are real and same\nx1 = x2 = %.2f",a,b,c,x1);
***  ***      *   * * *****
*   * * **  * *** *      *   *   * ** **   ** * * ***  * ** ***  
* * * * ***  **  *   * ** **
 * * *** *****  ***  ******   * *  * * *  ***     ******     *     of %.2fx^2 + %.2fx + %.2f = 0 are complex and different\nx1 = %.2f + %.2fi\nx2 = %.2f - ** ** **    * * * * 
**   *  ** **** *** *** ****** 
** *  * * **  **   *   *  * 0;
}