3, Solve forthe roots: x2 + 4-0 A math teacher needs to quiz students about solv
ID: 3747900 • Letter: 3
Question
3, Solve forthe roots: x2 + 4-0 A math teacher needs to quiz students about solving the about cheating, so she wants to give each student a one with complex roots. In each case, the roots will have September 16, 2018 quiz to so Name: roots, one with real roots, and L. Solve for the roots +4r+30 the Repeated roots: In the range -5 to 5, but cannot be 0. Real roots: Both in the range -5 to 5; the first root cannot be 0, the second cannot be the same as the first Complex roots: Real and imaginary parts in the range:-5 to 5; the imaginary part cannot be 0 Discriminant 42-4-1-3:16-11-4 (a) The quiz questions (for the student) b) The answer key (for the teacher) d> 0: Real Roots September 15, 2018 1. Solve for the roots: x24x+3 0 2-1.5-1=-25 2. Solve for the roots: x2+7x-2-0Explanation / Answer
#include <stdio.h>
#include <math.h>
void print_roots(int a, int b, int c){
double determinant, root1,root2, realPart, imaginaryPart;
determinant = b*b-4*a*c;
// condition for real and different roots
if (determinant > 0)
{
// sqrt() function returns square root
root1 = (-b+sqrt(determinant))/(2*a);
root2 = (-b-sqrt(determinant))/(2*a);
printf(" root1 = %.2lf and root2 = %.2lf ",root1 , root2);
}
//condition for real and equal roots
else if (determinant == 0)
{
root1 = root2 = -b/(2*a);
printf(" root1 = root2 = %.2lf; ", root1);
}
// if roots are not real
else
{
realPart = -b/(2*a);
imaginaryPart = sqrt(-determinant)/(2*a);
printf(" root1 = %.2lf+%.2lfi and root2 = %.2f-%.2fi ", realPart, imaginaryPart, realPart, imaginaryPart);
}
}
int main(void) {
// your code goes here
//for repeated roots-
/*
(x-a)(x-a)=0
x^2-a^2 x+a^2=0
-5<=a<=5
*/
printf(" For repeated roots -> ");
for(int a=-5;a<=5;a++){
printf(" x^2 - %d x + %d ", 2*a, a*a);
print_roots(1, 2*a, a*a);
}
//for real roots
//D>0
/*
(x-a)(x-b)=0
x-(a+b)x+ab=0
D=(a+b)^2-4ab
*/
printf(" For Real roots -> ");
for(int a=-5;a<=5;a++){
if(a==0)
continue;
for(int b=-5;b<=5;b++){
if(a==b){
break;
}
if(pow(a+b, 2)-4*a*b > 0){
printf(" x^2 - %d x + %d ", a+b, a*b);
print_roots(1, -1*(a+b), a*b);
}
}
}
//for imaginary roots
printf("For Imaginary roots roots -> ");
for(int b=-10; b<=10; b++){
if(b==0)
continue;
for(int a=-10; a<=10;a++){
if(a==0){
continue;
}
for(int c=-10; c<=10; c++){
if(c==0)
continue;
if((pow(b, 2)- 4*a*c)<0){
int x=-1*(pow(b, 2)-4*a*c);
if(-5<=sqrt(x)/2<=5){
printf(" %d x^2 + %d x + %d ", a, b, c);
print_roots(a, b, c);
}
}
}
}
}
return 0;
}
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