Question

Solve the polynomial inequality calculator

a) x < -3 or x > 2
b) x < -2 or x > 3
c) x < -3 or x > 3
d) x < -2 or x > 2

Answer 1

To solve a polynomial inequality, one does not simply use the quadratic formula directly. Instead, one should factor the polynomial and determine the intervals where the inequality holds true.

Step-by-step explanation:

The solution or roots for any quadratic equation can be calculated using the following formula:

x = −b ± √(b² - 4ac)
2a

When you apply this formula to a given quadratic equation of the form ax²+bx+c = 0, you are able to find the x-values that solve the equation. However, to address the specific question which relates to solving a polynomial inequality, you don't need to solve a quadratic equation directly. Instead, determining the intervals where the inequality holds is required.

The correct approach would involve factoring the polynomial if possible, and then analyzing the sign of the polynomial on intervals defined by the critical points (the values of x where the polynomial equals zero). These intervals correspond to the regions where the inequality is true (either less than 0 or greater than 0).