Αποτελέσματα Αναζήτησης
Pick the intervals where the graph corresponds to the inequality's symbol. For instance, if you are being asked to find where the polynomial is "greater than zero", then pick the interval(s) where the polynomial's graph is above the x-axis. Here's an example of solving a simpler polynomial inequality:
A polynomial inequality is an inequality where both sides of the inequality are polynomials. For example, x^3 \ge x^4 x3 ≥ x4 is a polynomial inequality which is satisfied if and only if 0 \le x \le 1. 0 ≤ x ≤ 1. These inequalities can give insight into the behavior of polynomials.
Within each interval between two adjacent critical points, the graph is either always above the \(x\)-axis, or always below the \(x\)-axis. Thus, finding the critical points of a polynomial inequality plays a fundamental role in solving a polynomial inequality.
The solution has to satisfy both inequalities \ (x\geq -1\)and\ (x>24\). Both inequalities are true for \ (x>24\) (since then also \ (x\geq -1\)), so that this is in fact the solution: \ (x>24\). When dealing with polynomial inequalities, we use the same three-step strategy that we used in section 1.4.
Solve the given inequality. 2x3 + 8x2 + 5x − 3 ≥ 0. First, we graph the function: Then we identify the intervals of x -values that make the y value greater than or equal to zero, as indicated in the problem. The indicated roots of the function (A, B and C) are the x -values that make y equal to zero.
16 Νοε 2022 · The first thing to do is get a zero on one side and factor the polynomial if possible. \[\begin{array}{c}{x^2} - 5x + 6 \ge 0\\ \left( {x - 3} \right)\left( {x - 2} \right) \ge 0\end{array}\] So, the polynomial will be zero at\(x = 2\) and \(x = 3\).
You can use the Mathway widget below to practice solving polynomial inequalities. Try the entered exercise, or type in your own exercise. Then click the button and select "Solve the Inequality for x" to compare your answer to Mathway's.
