Final answer:
The solution for the quadratic inequality x²+13x+42 > 0 is found by factoring it into (x+6)(x+7)>0. Then, we find where the factored inequality is positive or negative between the roots, -6 and -7. The solution is x<-7 or x>-6.
Step-by-step explanation:
The quadratic inequality in question is x²+13x+42 > 0. To solve this inequality, we first want to factor it down, giving us (x+6)(x+7)>0. The inequality is greater than zero, meaning we are looking for where the graph is above the x-axis. We find this by taking the roots (found by setting each factor to zero), -6 and -7, and plugging values that exist between these roots into the original inequality. The intervals we get are (-∞,-7),(-7,-6), and (-6,∞). Testing the intervals on the factored inequality finds the solution to be x<-7 or x>-6.
Learn more about Solving Nonlinear Inequalities