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Solve the polynomial inequality and graph the solution set on a real number line. Express the solution set...

Solve the polynomial inequality and graph the solution set on a real number line. Express the solution set in interval notation.
x^2 - 12x + 36 < 0
Solve the inequality. What is the solution set? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The solution set is [ ]
(Simplify your answer. Type your answer in interval notation. Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression.)
B. The solution set is the empty set.

Answer

The inequality is x^2 - 12x + 36 < 0.

First, factor the quadratic expression: (x - 6)^2 < 0.

Since (x - 6)^2 is always non-negative and equals zero when x = 6, there are no real numbers x that satisfy (x - 6)^2 < 0.

Answer: B. The solution set is the empty set.

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