If are real numbers such that , what can we say about ?
Hint: Think about the function .
For what values of are there no intersection points between the line and the circle ?
is uniformly chosen from the interval . Let be the probability that the quadratic has both roots between -2 and 4. What is the value of ?
Details and assumptions
Greatest Integer Function: refers to the greatest integer less than or equal to . For example and .
For how many positive integer values of c does the equation have an integer solution?
For a positive integer such that what is the probability that the quadratic equation has real roots?