Question

Polynomial Inequalities:

3) 4x - x^2 > 0

show your number line test and state answer in interval notation

Answer 1

Let us solve the equality $4x - x^2 > 0,$ which is equivalent to $x(4 - x) > 0.$ The equation $x(4 - x) =0$ has two roots $x_1=0,\ x_2=4.$

Let us use number line test. For this draw the following intervals:

Since $4(-1)-(-1)^2=-5<0,\ 4\cdot 1-1^2=3>0,$ and $4\cdot 5-5^2=-5<0,$ we conclude that the solutions of the inequality belongs to the real interval $(0,4).$