A: What are the solutions to the quadratic equation x2+49=0?

Question

B: What is the factored form of the quadratic expression x2+49?

Select one answer for question A, and select one answer for question B.
B: (x−7i)(x−7i)
A: x=7i
B: (x+7)(x−7)
A: x=7 or x=−7
A: x=−7
B: (x+7)(x+7)
A: x=7i or x=−7i
B: (x+7i)(x−7i)

Answer 1

A: x=7i or x=−7i
B: (x+7i)(x−7i)

Answer 2

A. x^2 + 49 = 0.
x^2 = -49.
X = sqrt (-49) = sqrt(49*(-1)) = 7i. No real solution.

B. (x+7i)(x-7i).

Answer 3

A.

x² + 49 = 0

Subtract 49 from both sides

x² + 49 - 49 = 0 - 49

x² = - 49

x = √ - 49

x = ± √ [ ( - 1) ∙ 7² ]

x = ± √ ( - 1) ∙ √ 7²

x = ± i ∙ 7

x = ± 7 i

The solutions are

x = - 7 i and x = 7 i

B.

a x² + bx + c = a ( x - x1 ) ∙ ( x - x2 )

in this case

a = 1 , b = 0 , c = 49 , x1 = - 7 i , x2 = 7 i

x² + 49 = 1 ∙ [ x - ( - 7 i ) ∙ ( x - 7 i ) ]

x² + 49 = ( x + 7i ) ∙ ( x - 7 i )

x² + 49 = ( x - 7 i ) ∙ ( x + 7 i )