Polynomial Inequalities
Polynomial inequalities constitute a fundamental concept in algebra, offering a framework for understanding the behavior of polynomial functions across intervals. These inequalities express relationships between polynomial expressions and real numbers, revealing the intervals where the polynomial function is positive, negative, increasing, or decreasing. By analyzing the signs of polynomial expressions and their factors, mathematicians can determine the solutions to polynomial inequalities and sketch their corresponding graphs. This introductory exploration lays the groundwork for delving into more complex topics within algebra and calculus, highlighting the practical applications of polynomial inequalities in various mathematical and scientific contexts.
- How do you solve #x/(x-3)>0#?
- How do you solve the inequality #-x^2+14x-49>=0#?
- How do you solve #-x^2+x+5>0# by graphing?
- How do you solve #x/(x-1)>2#?
- How do you solve the inequality #6x^2-5x>6#?
- How do you solve #8r-r^2>=15#?
- How do you solve #(x+4)/x>0#?
- How do you solve #x^4+8x^3+15x^2-4x-20<0#?
- How do you solve #-s^2+4s-6<0#?
- How do you graph #y < x^2- 5x#?
- How do you solve #sqrt(2x-7)>=5#?
- How do you solve #x^3-5x^2<x-5# using a sign chart?
- How do you solve the inequality #9x^2-6x+1<=0#?
- How do you solve #x^3+2x^2-4x-8>=0# using a sign chart?
- How do you solve #15-2y-y^2<=0#?
- How do you solve #(5-x)^2(x-13/2)<0#?
- How do you solve #(4-2x)/(3x+4)<=0#?
- The roots of the polynomial equation #2x^3-8x^2+3x+5=0# are #alpha#, #beta# and #gamma#. What is the polynomial equation with roots #alpha^2#, #beta^2# and #gamma^2#?
- How do you resolve the following inequality: #((x^2-4)(3x-6))/(x-7)>0#?
- How do you solve #x^3<=4x^2# using a sign chart?