Option A
The solution is:
[tex]x = \pm 2i \sqrt{2}[/tex]
Solution:
[tex]f(x) = 19x^2+152[/tex]
We have to solve the equation f(x) = 0
Let f(x) = 0
[tex]0=19x^2+152[/tex]
Solve the above equation
[tex]19x^2 + 152 = 0[/tex]
[tex]\mathrm{Subtract\:}152\mathrm{\:from\:both\:sides}\\\\19x^2+152-152=0-152\\\\Simplify\ the\ above\ equation\\\\19x^2 = -152\\\\\mathrm{Divide\:both\:sides\:by\:}19\\\\\frac{19x^2}{19} = \frac{-152}{19}\\\\x^2 = -8[/tex]
Take square root on both sides
[tex]x = \pm \sqrt{-8}\\\\x = \pm \sqrt{-1}\sqrt{8}\\\\\mathrm{Apply\:imaginary\:number\:rule}:\quad \sqrt{-1}=i\\\\x = \pm i\sqrt{8}\\\\x = \pm i \sqrt{2 \times 2 \times 2}\\\\x = \pm 2i\sqrt{2}[/tex]
Thus the solution is found