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

Question

17k 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 | 17k 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;
}