SOLVE BY HAND SOLVE BY HAND 1894x134x25x30 can you solve by

SOLVE BY HAND SOLVE BY HAND

1.8-9.4x-13.4x²-5x³=0

can you solve by hand (Simple Method

Let ,g(x)=1.8-9.4x-13.4x^2-5x^3

g(0)=1.8

g(1)=1.8-9.4-13.4-5<0

Since g is continuous function so it has a root int he interval (0,1)

We find this root approximately using bisection method.

x_1=(0+1)/2=0.5,g(x_1)=-6.875<0

SO there is a root in the interval: (0,0.5)

x_2=(0+0.5)/2=0.25,g(x_2)=-1.465625<0

Hence there is root in the interval: (0,0.25)

x_3=(0+0.25)/2=0.125,g(x_3)=0.405859>0

Hence there is root in the interval: (0.125,0.25)

x_4=(0.125+0.25)/2=0.1875,g(x_4)=-0.4666<0

HEnce there is root in the interval: (0.125,0.1875)

x_5=(0.125+0.1875)/2=0.15625,g(x_5)=-0.01497<0

Hence there is root in the interval: (0.125,0.15625)

x_6=(0.125+0.15625)/2=0.140625,g(x_6)=0.19923>0

So there is root in the interval:(0.140625,0.15625)

x_7=.1484375,g(x_7)=0.0983

And so on. WE can keep iterating till g(x_n) is sufficiently close to 0

So approximate root is:x=0.1484375