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

Question

Solve the polynomial inequality and graph the solution set on a real number line. Express the solution set in interval notation.
x^2 - 9x + 14 > 0
A. The solution set is (-∞,2)∪(7,∞).
(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.
Choose the correct graph below:

SnapAndSolve AI · Accepted Answer

To solve the inequality x^2 - 9x + 14 > 0, we first find the roots of the equation x^2 - 9x + 14 = 0. Factoring, we get (x - 2)(x - 7) = 0, so the roots are x = 2 and x = 7.

The inequality x^2 - 9x + 14 > 0 is satisfied when x < 2 or x > 7. Therefore, the solution set in interval notation is (-∞, 2) ∪ (7, ∞).

The correct graph is option A, which shows the intervals (-∞, 2) and (7, ∞) on the number line.

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

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