3.
Which of the following is a solution of x² + 14x + 112 = 0? If necessary, round to the nearest hundredth.
A.) x = –0.24
B.) x = –4.24
C.) 4.24
*D.) no solution
Thank you
x=(-14+-sqrt(256-4*112) )/2
since the serd is sqrt (-192), there is a solution, but it is not a real number.
answer e) no real solution should have been the right answer.
c
b
d
b
To determine which of the given options is a solution to the equation x² + 14x + 112 = 0, we can use the quadratic formula. The quadratic formula states that for an equation of the form ax² + bx + c = 0, the solutions for x can be found using the formula:
x = (-b ± √(b² - 4ac)) / (2a)
Comparing this formula with the equation x² + 14x + 112 = 0, we can see that a = 1, b = 14, and c = 112. Substituting these values into the quadratic formula, we get:
x = (-14 ± √(14² - 4(1)(112))) / (2(1))
Simplifying further:
x = (-14 ± √(196 - 448)) / 2
x = (-14 ± √(-252)) / 2
Since the expression within the square root (√(-252)) is negative, it means that the square root is an imaginary number. In this case, it implies that the equation x² + 14x + 112 = 0 has no real solutions, and the answer is option D) no solution.