Which of the following is a solution of x^2 + 14x + 112 = 0? If necessary round to the nearest hundredth.
a. x = -0.24
b. x = -4.24
c. x = 4.24
d. There is no solution
First, we need to find the solutions of the quadratic equation x^2 + 14x + 112 = 0 by using the quadratic formula. The quadratic formula is given by x = [-b ± √(b^2 - 4ac)] / 2a.
In this case, the coefficients are a = 1, b = 14, and c = 112. Plugging these into the formula:
x = [-14 ± √(14^2 - 4*1*112)] / 2*1
x = [-14 ± √(196 - 448)] / 2
x = [-14 ± √(-252)] / 2
x = [-14 ± 15.87i] / 2
x = -7 ± 7.93i
Therefore, the solutions are imaginary and there is no real number solution for this equation.
The correct answer is: d. There is no solution.