1 The discriminant of a quadratic function is b2 - 4ac.
Given a quadratic equation in the form ax? + b + c,
if b2
4ac > 0, then the equation has two real solutions.
if b2 - 4ac = 0, then the equation has one real solutions.
if b2 - 4ac <0, then the equation has no real solutions.
Use the discriminant to determine the number of solutions for 10x2 - 4x + 1
a
be
Since b^2 - 4ac is
- greater than 0,
- equal to 0,
- less than 0,
the equation has
- two real solution
- one real solution
- no real solution

An oil exploration company currently has two active projects, one in asia and the other in europe. let a be the event that the asian project is successful and b be the event that the european project is successful. suppose that a and b are independent events with p(a) = 0.2 and p(b) = 0.8. (a) if the asian project is not successful, what is the probability that the european project is also not successful? (b) what is the probability that at least one of the two projects will be successful? (c) given that at least one of the two projects is successful, what is the probability that only the asian project is successful? (round your answer to three decimal places.)