Answer:
Solution of given quadratic equation is
[tex]$ (\frac{8i}{3}, -\frac{8i}{3} ) $[/tex]
Step-by-step explanation:
The given quadratic equation is
[tex]9x^2 + 64 = 0[/tex]
The general form of the quadratic equation is given by
[tex]ax^2 + bx + c = 0[/tex]
Comparing the general form with the given quadratic equation
[tex]a = 9\\b = 0\\c = 64[/tex]
The solutions of the quadratic equation is given by
[tex]$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$[/tex]
Substitute the values of a, b and c
[tex]$x=\frac{-0\pm\sqrt{0^2-4(9)(64)}}{2(9)}$[/tex]
[tex]$x=\frac{\pm\sqrt{-2304}}{18}$[/tex]
[tex]$x=\frac{\pm48i}{18}$[/tex]
[tex]$x=\frac{\pm8i}{3}$[/tex]
[tex]$x=\frac{8i}{3}$[/tex]
and
[tex]$x=-\frac{8i}{3}$[/tex]
Where i represents iota which means that the given quadratic equation has complex roots.
So the solution of given quadratic equation is
[tex]$ (\frac{8i}{3}, -\frac{8i}{3} ) $[/tex]
The factored form of the given quadratic equation is
[tex]$ (x+ \frac{8i}{3}) (x- \frac{8i}{3}) = 0 $[/tex]
