Question

Solve 2x2 − 6x = −8.

negative 3 plus or minus 5i all over 2
the quantity of 3 plus or minus 2i square root 30 all over 2
the quantity of 3 plus or minus i square root 30 all over 2
the quantity of 3 plus or minus i square root 7 all over 2

Answer 1

2x²-6x+8=0
x²-3x+4=0
D=b²-4ac=9-16=-7
x=(3+/-i√7)/2
correct answer is the last one

Answer 2

Option 4 - the quantity of 3 plus or minus i square root 7 all over 2

Explanation:

Given : Expression
`2x^2-6x=-8`

To find : The solution of the expression ?

Solution :

Expression
`2x^2-6x=-8` can be written as

`2x^2-6x+8=0`

`x^2-3x+4=0`

Solve by quadratic formula,

The general form of quadratic equation is
`ax^2+bx+c=0` with solution
`x=(-b\pm√(b^2-4ac))/(2a)`

On comparing with
`x^2-3x+4=0`, a=1 , b=-3, c=4

Substitute in solution,

`x=(-b\pm√(b^2-4ac))/(2a)`

`x=(-(-3)\pm√((-3)^2-4(1)(4)))/(2(1))`

`x=(3\pm√(9-16))/(2)`

`x=(3\pm√(-7))/(2)`

`x=(3\pmi√(7))/(2)`

So, The solution is the quantity of 3 plus or minus i square root 7 all over 2.

Therefore, Option 4 is correct.