Question

For question 25 please pick 1,2,3 or 4

Answer 1

4.

`$x=(2)/(3) \pm (1)/(6)i √(158)$`

Explanation:

`18x^2-24x+87=0`

Using Quadratic Formula

`$x=(-b\pm √(b^2-4ac))/(2a)$`

`$x=(-\left(-24\right)\pm √(\left(-24\right)^2-4\cdot \:18\cdot \:87))/(2\cdot \:18)$`

Solving the discriminant:

`\Delta = \left(-24\right)^2-4\cdot \:18\cdot \:87\\\Delta = 576-6264\\ \Delta=-5688`

`$x= (24 \pm √(-5688) )/(36) $`

`$x= (24 \pm √(5688i) )/(36) $`

Once
`√(5688) =√(2^3\cdot \:3^2\cdot \:79)=6√(158)`

`$x=(24\pm6√(158)i)/(36)$`

Dividing the denominator and numerator by 6

`$x=(4\pm √(158)i)/(6)$`

Now rewrite it:

`$x=(4)/(6) \pm i(√(158))/(6)$`

`$x=(2)/(3) \pm i (√(158))/(6)$`

or

`$x=(2)/(3) \pm (1)/(6)i √(158)$`