Question

Newton-Raphson method is used to compute a root of the equation $2x^2+5x-9=0$ with 4.5 as the initial value. The approximation after one iteration is ________

• A. 2.15

Answer 1

The correct option is A 2.15
The equation is $f\left(x\right)=2x^2+5x-9=0$
Newton-Raphson iteration equation is
$x_1=x_0-\left[\frac{f\left(x_0\right)}{f^{{}^{\prime }}\left(x_0\right)}\right]$
$f\left(x_0\right)=2x_0^2+5x_0-9$
$f^{{}^{\prime }}\left(x_0\right)=4x_0+5$
$\therefore x_1=x_0-\left[\frac{2x_0^2+5x_0-9}{4x_0+5}\right]$
$=\frac{4x_0^2+5x_0-2x_0^2-5x_0+9}{4x_0+5}$
$=\frac{2x_0^2+9}{4x_0+5}$
Put $x_0=4.5$ (as given)
$x_1=\frac{2\times (4.5{)}^2+9}{4\times \left(4.5\right)+5}=2.15$