# SOLUTION: Question: x^2+5x>24 Possible Answers: a. none of these b. -3<x<8 c. x<-3 or x>8 d. X<-8 or x>3

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 Click here to see ALL problems on Linear Algebra Question 30152: Question: x^2+5x>24 Possible Answers: a. none of these b. -3 c. x<-3 or x>8 d. X<-8 or x>3Answer by sdmmadam@yahoo.com(530)   (Show Source): You can put this solution on YOUR website!x^2+5x>24 That is x^2+5x-24 > 0 (x+8)(x-3) > 0 Since either positive multiplied by positive is positive OR negative multiplied by negative is positive, there are two cases. Case 1: Let (x+8) > 0 together with (x-3) > 0 This implies x > -8 together with x > 3 And since anything to the right of 3 is definitely to the right of (-8), the verdict for this case is x > 3 Case 2: Let (x+8) < 0 together with (x-3) < 0 This implies x < -8 together with x < 3 And since anything to the left of (-8) is definitely to the left of 3, the verdict for this case is x < -8 Therefore combining the results of both the cases we have Answer: x< -8 and x > 3 Which is your choice (d) Note: (factoring the quadratic expression: x^2+5x-24, product =(-24) and sum is 5 and therefore the quantities are (+8) and (-5) and therefore x^2+5x-24 = x^2+(8x-3x)-24 = (x^2+8x)-3x-24 =x(x+8)-3(x+8) =xp-3p where p = (x+8) =p(x-3) =(x+8)(x-3)