Metodos

public class Biseccion {
public static double funcion(double a){
double f = 0;
f = -12*Math.pow((double)a, 5)-6*Math.pow(a, 3)+10;
return f;
}

publicstatic double error (double x, double y){
double e = (Math.abs(x - y) / x)*100;
return e;
}

public static void main(String[] args) {

double fa = 0,fb, fx, xr = 0, xrAnt, a, b, e;
boolean flag = false;
a = 0;
b = 1;
e = 0;

for (int i = 0; i < 10; i++) {
if(i > 0)flag = true;
xrAnt = xr;


fa = Biseccion.funcion(a);
fb = Biseccion.funcion(b);
xr = (a+b)/2;
fx =Biseccion.funcion(xr);

if (fa*fx<0){
a = a;
b = xr;
}else{
a = xr;
b = b;
}System.out.println("a: "+a+" b:"+ b +" fa:"+fa+" fb: "+fb);
if(flag){
e = error(xr, xrAnt);
System.out.println("Error: " +e);
if(e < 5)
System.exit(0);
}

}
}
}

Resultados Programa
a: 0.5 b:1.0 fa:10.0 fb: -8.0
a: 0.75 b:1.0fa:8.875 fb: -8.0
Error: 33.33333333333333
a: 0.75 b:0.875 fa:4.62109375 fb: -8.0
Error: 14.285714285714285
a: 0.8125 b:0.875 fa:4.62109375 fb: -0.1744384765625
Error:7.6923076923076925
a: 0.84375 b:0.875 fa:2.5326271057128906 fb: -0.1744384765625
Error: 3.7037037037037033

Captura Pantalla Resultados.
Resultados Excel
No. Iteración | a | b | f(a) | f(b) | XR |f(XR) | ep |
1 | 0.000000 | 1.000000 | 10 | -8 | 0.500000 | 8.875 |   |
2 | 0.500000 | 1.000000 | 8.875 | -8 | 0.750000 | 4.62109375 | 33.333333 |
3 | 0.750000 | 1.000000 | 4.62109375 | -8 |...