Solve the following inequality.
\[
x^{2}-14 x+40< 0
\]
Select the correct choice below and, if necessary, fill in the answer box.
A. The solution set is
(Type your answer in interval notation. Use integers or fractions for any numbers in the expression.)
B. There is no real solution.
Answer
\(\boxed{\text{The solution set is } (4, 10)}\)
Step 1 ：The given inequality is a quadratic inequality. To solve it, we first need to factorize the quadratic expression on the left side of the inequality.
Step 2 ：The factored inequality is \((x - 10)*(x - 4) < 0\).
Step 3 ：We then find the roots of the quadratic equation obtained by setting the expression equal to zero. The roots of the quadratic equation are 4 and 10.
Step 4 ：These roots divide the number line into three intervals: (-∞, 4), (4, 10), and (10, ∞).
Step 5 ：We then test the sign of the expression in each interval. The sign of the expression in each interval is positive, negative, and positive, respectively.
Step 6 ：Therefore, the expression is less than zero in the interval (4, 10).
Step 7 ：\(\boxed{\text{The solution set is } (4, 10)}\)
