Question

What is the solution to the following equation?

x² + 3x + 7 = 0

A. x= 3+-√25/2
B. x= -3+-√37/2
C. x= -3+-√²7/2
D. x= -3+-√-19/2

Answer 1

Answer: D

Step-by-step explanation:

Answer 2

Answer: Choice D

`x = (-3\pm√(-19))/(2)\\\\`

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Step-by-step explanation:

Compare the given equation x² + 3x + 7 = 0 to ax² + bx + c = 0 to find that,

• a = 1
• b = 3
• c = 7

Those values are plugged into the quadratic formula to get the following:

`x = (-b\pm√(b^2-4ac))/(2a)\\\\x = (-3\pm√((3)^2-4(1)(7)))/(2(1))\\\\x = (-3\pm√(-19))/(2)\\\\`

which points us to choice D being the final answer.

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Side note:

The discriminant
`d = b^2 - 4ac = (3)^2-4(1)(7) = -19` is negative, so there are no real solutions. Instead, the two solutions are non-real complex numbers.