This document contains code to solve quadratic equations and find roots of functions using the bisection method. The quadratic equation code calculates the discriminant and uses it to determine the number and type of roots, printing the result. The bisection method code iteratively calculates the midpoint between guesses for a root and determines if the next guess should be the lower or upper value based on the sign of the function at each point until convergence within a set tolerance.

2.  Quadractic Equation
 Bisection Method

3. int main()
{
float a,b,c,D,x,y;
clrscr();
printf(“Enter the coefficient of x2, coefficient of x and constant”);
scanf(“%f%f”,&a, &b, &c);
D=(b*b)-(4*a*c);
if(D<0)
{
printf(“Roots are Imagenary”);
}
if(D==0)
{
printf(“Both Roots are Same”);
x =(-b)/(2*a);
printf(“%f”, x);
}
if(D>0)
{
printf(“Both Roots are Real and Distinct:”);
x= (-b) + sqrt(D)/2*a;
y= (-b) - sqrt(D)/2*a;
printf(“%f%f”, x,y);
}
getch();
return 0;
}

4. #include<stdio.h>
#define e 0.001
#define f(x) x*x*x -4*x +1
void main()
{
float x0,x1,x2;
float f0,f1,f2;
clrscr();
printf(“Enter the values of x0 and x1”);
scanf(“%f%f”,&x0,&x1);
do{
f0 = f(x0);
f1 = f(x1);
x2=(x0+x1)/2;
f2=f(x2);
if(f0*f2<0)
{
x1=x2;
}
else
{
x0=x2;
}
i++;
printf(“No. of Iterations:=%d”,i);
printf(“Root:=%f”,x2);
printf(“Value of function =%fn”,f2);
}while(fabs(f2)<e);
getch();