Question

What are the solutions of 2x2 + 3x= −8? (6 points) Select one: a. the quantity negative 3 plus or minus i square root of 41 all over 4 b. the quantity negative 3 plus or minus i square root of 55 all over 4 c. the quantity negative 3 plus or minus i square root of 21 all over 4 d. the quantity negative 3 plus or minus i square root of 15 all over 4

Answer 1

2x²+3x+8=0
this cannot be factored, so use the quadratic formula to solve:
x=[-b+√(b²-4ac)]/(2a) or x=[-b-√(b²-4ac)]/(2a), a=2, b=3, c=8 in this case
3²-4*2*8=-55
the answer is b.

Answer 2

Option b -
`x=(-3\pm√(55)i)/(4)`

Explanation:

Given : Equation
`2x^2+3x=-8`

To find : What are the solutions of equation ?

Solution :

Re-write the equation as,

`2x^2+3x+8=0`

Solving by quadratic formula,
`x=(-b\pm√(b^2-4ac))/(2a)`

Here, a=2, b=3 and c=8

`x=(-3\pm√(3^2-4(2)(8)))/(2(2))`

`x=(-3\pm√(9-64))/(4)`

`x=(-3\pm√(-55))/(4)`

`x=(-3\pm√(55)i)/(4)`

Therefore, the solution is
`x=(-3\pm√(55)i)/(4)`

So, option b is correct.