Problem

For the function $f(x)=x^{2}+5 x-36$ solve the following. \[ f(x) \leq 0 \] Select the correct choice below and fill in the answer box within your choice. A. The solution is (Use a comma to separate answers as needed.) B. The solution is (Type your answer in interval notation.)

Solution

Step 1 :Factor the quadratic expression on the left side of the inequality, which gives \((x - 4)(x + 9)\).

Step 2 :Build a sign chart to determine the signs of the factors and the product in different intervals.

Step 3 :From the sign chart, we can see that \(x^2 + 5x - 36\) is less than or equal to 0 when \(-9 < x < 4\).

Step 4 :Also, \(f(x) = 0\) at \(x = 4\) and \(x = -9\).

Step 5 :Thus, the solution is \(x \in \boxed{[-9,4]}\).

From Solvely APP
Source: https://solvelyapp.com/problems/46289/

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