Question

Solve the following quadratic inequality. Express the solution on a number line and using interval notation x²-x>=42

Answer 1

To solve the quadratic inequality x²-x>=42, we rewrite it in the form ax²+bx+c>0, factor the quadratic expression, and determine the intervals where the expression is greater than zero.

Step-by-step explanation:

To solve the quadratic inequality x²-x>=42, we first need to rewrite it in the form ax²+bx+c>0. So, subtracting 42 from both sides, we get x²-x-42>0. Next, we factor the quadratic expression to find the solutions by setting each factor equal to zero. Factoring gives us (x-7)(x+6)>0. Now, we can determine the intervals where the expression is greater than zero by constructing a sign chart or by using test points method. The solution is x<-6 or x>7.