- #1

karush

Gold Member

MHB

- 3,269

- 5

Find x for $f(x)=0 \quad 5+i\quad 5-i\quad $

$\begin{array}{rl}

\textsf{factored} &f(x)=(x-1)[x-(5+i))(x-(5-i)]\\

\textsf{foil} &x^2-x(5+i)-x(5-i)+(5-i)^2\\

\textsf{expand} &x^2-5x-xi-5x+xi+25-2i+i^2 \\

\textsf{simplify} &x^2-10x+26\\

\textsf{observation } &(x-1)=0,\quad x=1\\

\textsf{quadratic formula} &=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\

&=\dfrac{-(10)\pm\sqrt{(10)^2-4(1)(26)}}{2(1)}\\

&=\dfrac{-1\pm\sqrt{100-96}}{2}

=\dfrac{-10\pm2i}{2}=5\pm i

\end{array}$

can't seem to get the errors out of this;)