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

Answer:

Option b - $x=\frac{-3\pm\sqrt{55}i}{4}$

Step-by-step 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, $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

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

$x=\frac{-3\pm\sqrt{3^2-4(2)(8)}}{2(2)}$

$x=\frac{-3\pm\sqrt{9-64}}{4}$

$x=\frac{-3\pm\sqrt{-55}}{4}$

$x=\frac{-3\pm\sqrt{55}i}{4}$

Therefore, the solution is $x=\frac{-3\pm\sqrt{55}i}{4}$

So, option b is correct.