identify solution set

Question

Identify the solution set to the quadratic inequality x^2-x-12(greater than or equal to) 0. 

The solution set is __. 

(Type your answer in interval notation.) 

 

need this one last question to be done with my homework, answers are greatly appreciated! 

Answer 1

The key to this problem is to identify when quadratic is equivalent to zero and we know that if y = x² - x - 12, then when y ≥ 0, we have the inequality hold true.

 

y = 0

x² - x - 12 = 0

(x-4)(x+3) = 0

when x = 4, -3 we have that y = 0.

 

whenever x > 4 or x < -3. We will have y > 0. thus the solution set is:

 

x ∈ (-∞,-3] , [4, ∞)  (x is contained in the two ranges).