Solve the following inequality.
x^2 +16x+60<0
Select the correct choice below and, if necessary, fill in the answer box.
A.The solution set is
B.There is no real solution
The given inequality is x^2 + 16x + 60 < 0.
To solve this inequality, we first find the roots of the corresponding equation x^2 + 16x + 60 = 0 by factorizing or using the quadratic formula.
The roots are (-6) and (-10), so the inequality changes signs at these points.
Next, we choose test points from both intervals (-∞, -10) and (-10, -6) to see which interval satisfies the inequality.
Choosing x = -11, we get (-11)^2 + 16(-11) + 60 = 121 - 11*16 + 60 = 121 - 176 + 60 = 5 - 176 = -171 < 0.
Therefore, the solution is:
-10 < x < -6.
The correct choice is:
A. The solution set is (-10, -6).