Question

Ind the solution set of the quadratic equation over the set of complex numbers.

5x2 + 12x + 8 = 0

Answer 1

hello :
5x²+12x+8 =0
delta = 12²-4(5)(8) = -16 = 16i²......(i² = 1)
delta = (4i)²
x1 = (-12+4i)/2 x2 = (-12-4i)/2
x1 =-6+2i x2 = -6-2i

Answer 2

`S=\{ (-6)/(5)+(2)/(5)i, (-6)/(5)-(2)/(5)i\}`

Explanation:

`5x^2+12x+8 =0`

We are going to use the general formula to find the solution. That formula is

`x = (-b\pm√(b^2-4ac))/(2a)`

where a= 5, b=12 and c=8. Then

`x = (-12\pm√(144-4(5)(8)))/(10)`

`x = (-12\pm√(144-4(5)(8)))/(10)`

`x = (-12\pm√(-16))/(10)`

`x = (-12\pm4i)/(10)`

`x_1 = (-12+4i)/(10)`

`x_1 = (-6)/(5)+(2)/(5)i`

`x_2 = (-12-4i)/(10)`

`x_2 = (-6)/(5)-(2)/(5)i`.

Then, the solution set is
`S=\{ (-6)/(5)+(2)/(5)i, (-6)/(5)-(2)/(5)i\}`