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

Question

12k 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 | 12k 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;
}