False Position Method

// FALSE POSITION METHOD

# include <stdio.h>
# include <math.h>

double a,b,c;

double initial_upper_value() {
    return sqrt( (b/a)*(b/a) - 2*(c/a) );
}

double evaluate( double x ) {
    return a*x*x + b*x + c;
}

int main() {
    printf( "Ax2 + Bx+ C = 0\n" );

    // input
    printf( "A = " );
    scanf( "%lf", &a );

    printf( "B = " );
    scanf( "%lf", &b );

    printf( "C = " );
    scanf( "%lf", &c );

    double x1, x2;
    // collecting initial limits
    x2 = initial_upper_value();
    x1 = -x2;

    int counter=0;
    double x;
    while( counter<1000 ) {
        x = x1 - ( ( evaluate(x1)*(x2-x1) ) / ( evaluate(x2)-evaluate(x1) ) );

        if( evaluate(x)==0 ) { counter=-10; break; }
        else if( evaluate(x1)*evaluate(x) < 0 ) x2=x;
        else x1=x;

        counter++;
    }

    if( counter<0 ) printf( "Root is = %lf\n", x );
    else printf( "Approximate root is = %lf\n", x );

    return 0;
}