Question

Given that f(x) = 19x2 + 152, solve the equation f(x) = 0

x = ±2isquare root of 2


x = ±2isquare root of 3


x = ±3isquare root of 2


x = ±4isquare root of 3

Answer 1

Option A

The solution is:

`x = \pm 2i √(2)`

Solution:

`f(x) = 19x^2+152`

We have to solve the equation f(x) = 0

Let f(x) = 0

`0=19x^2+152`

Solve the above equation

`19x^2 + 152 = 0`

`\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\\\\(19x^2)/(19) = (-152)/(19)\\\\x^2 = -8`

Take square root on both sides

`x = \pm √(-8)\\\\x = \pm √(-1)√(8)\\\\\mathrm{Apply\:imaginary\:number\:rule}:\quad √(-1)=i\\\\x = \pm i√(8)\\\\x = \pm i √(2 * 2 * 2)\\\\x = \pm 2i√(2)`

Thus the solution is found