Questions: Solve the polynomial inequality and graph the solution set on a real number line. Express the solution set in interval notation. x^2-18x+81<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.

Solve the polynomial inequality and graph the solution set on a real number line. Express the solution set in interval notation. x^2-18x+81<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.
Transcript text: Save Solve the polynomial inequality and graph the solution set on a real number line. Express the solution set in interval notation. \[ x^{2}-18 x+81<0 \] 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 $\square$ . (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.
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Solution

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Solution Steps

Step 1: Solve the Quadratic Equation

The given inequality is: \[ x^2 - 18x + 81 < 0 \]

First, solve the equation \(x^2 - 18x + 81 = 0\) to find the critical points. This is a perfect square trinomial: \[ (x - 9)^2 = 0 \]

The solution to this equation is: \[ x = 9 \]

Step 2: Analyze the Inequality

Since \((x - 9)^2\) is always non-negative and equals zero at \(x = 9\), the expression \(x^2 - 18x + 81\) is never less than zero. Therefore, the inequality \(x^2 - 18x + 81 < 0\) has no solution.

Final Answer

B. The solution set is the empty set.

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