Answer to Question #236776 in Calculus for CCW

Question #236776

Polynomial Inequalities:

3) 4x - x^2 > 0

show your number line test and state answer in interval notation


1
Expert's answer
2021-09-20T16:12:39-0400

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)."


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