What is the solution set of the inequality x^2-x>20?
a)x>5
b)-4<x<5
c)x>5 or x<-4
d)x>0
Factor x^2 -x -20 = 0
There are zeroes at x= 5 and x = -4.
In between -4 and 5, x^2 -x is less than 20. Therefore the answer is not b)
Take it from there
please help more
The Answer in c - x>5 or x<-4
as when x is less than -4 the inequality holds true as well as when x is greater than 5 it is still true.
To find the solution set of the inequality x^2 - x > 20, let's break it down step by step.
Step 1: Move all terms to one side of the inequality to have it in the equation form:
x^2 - x - 20 > 0
Step 2: Factorize the quadratic equation:
(x - 5)(x + 4) > 0
Step 3: Determine the sign of each factor to identify the intervals where the expression is positive (greater than 0).
- For (x - 5) > 0, x > 5
- For (x + 4) > 0, x > -4
Step 4: Combine the intervals where the expression is positive (greater than 0).
The combined solution set is x > 5 and x > -4.
However, when we analyze the overlapping regions, we can see that the solution set is x > 5 or x < -4. So, the correct answer is option c) x > 5 or x < -4.