A: What are the solutions to the quadratic equation x2+49=0?
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)
A: x=7i or x=−7i
B: (x+7i)(x−7i)
A. x^2 + 49 = 0.
x^2 = -49.
X = sqrt (-49) = sqrt(49*(-1)) = 7i. No real solution.
B. (x+7i)(x-7i).
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 )
A: The solutions to the quadratic equation x^2 + 49 = 0 can be found by isolating the variable x and taking its square root. First, subtract 49 from both sides of the equation to get x^2 = -49. Then, take the square root of both sides, considering both the positive and negative square roots. Therefore, the solutions are x = 7i and x = -7i.
B: The factored form of the quadratic expression x^2 + 49 is obtained by identifying the factors that multiply to give the expression. In this case, since 49 is a perfect square, we can factor it as the product of two identical factors. Therefore, the factored form is (x + 7i)(x - 7i).