Question

The second approximation of roots of $x^3-5x-7=0$ in the interval $(2,3)$ by the method of false position is?

• A. $1.735$
• B. $2.375$
• C. $3.735$
• D. $2.735$

Answer 1

The correct option is D $2.735$

Here, $x^3-5x-7=0$

Let $f\left(x\right)=x^3-5x-7$

First Iteration:

Here, $f\left(2\right)=-9<0$ and $f\left(3\right)=5>0$

Now, Root lies between $x_0=2$ and $x_1=3$

$x_2=x_0-f\left(x_0\right)\times \frac{x_1-x_0}{f\left(x_1\right)-f\left(x_0\right)}=2-(-9)\times \frac{3-2}{5-(-9)}=2.64286$

Second Iteration:

Here, $f\left(2.64286\right)=-1.75474$ and $f\left(3\right)=5>0$

Now, Root lies between $x_0=2.64286$ and $x_1=3$

$x_3=x_0-f\left(x_0\right)\times \frac{x_1-x_0}{f\left(x_1\right)-f\left(x_0\right)}=2.64-(-1.75)\times \frac{3-2.64}{5-(-1.75)}=2.73564$