SOLUTION: The pare of the Quadratic formula,{{{b^2-4ac}}}that is under the radical is called the discriminant. Complete the following sentences to show how this value indicates whether there

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: The pare of the Quadratic formula,{{{b^2-4ac}}}that is under the radical is called the discriminant. Complete the following sentences to show how this value indicates whether there      Log On


   

Question 74863This question is from textbook Beginning Algebra
: The pare of the Quadratic formula,b%5E2-4acthat is under the radical is called the discriminant. Complete the following sentences to show how this value indicates whether there are no solutions, one solution, or two solutions for the quadratic equation.
A) When b^2-4ac is _________________, there are no real number soulutions because......
B) When b^2-4ac is _________________, there is one solution because.....
C)When b^2-4ac is __________________, there are two solutions because.....
D)When b^2-4ac is __________________, there are two rational solutions because.....
E)When b^2-4ac is __________________, there are two irrational solutions because.....
I am really needing some help with this. I searched the internet for the answers, and now I am really confused. please help. Thanks This question is from textbook Beginning Algebra

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
A)
When b%5E2-4ac%3C0 there are no real solutions because if you have sqrt%28x%29 and x is a negative number, you wont have a real answer. You will have a complex solution. The reason why is because x%5E2 is always positive.


B)
When b^2-4ac is equal to zero, there is one solution because if you have
%286%2B-sqrt%280%29%29%2F2 you get %286%2B-0%29%2F2 and since zero has no sign, there is only one answer which in this case it's 3


D)
When b^2-4ac is equal to a perfect square (ie 9), there are two rational solutions because a perfect square is a rational number. For instance, if we have
%286%2B-sqrt%289%29%29%2F2 it equals %286%2B3%29%2F2 and %286-3%29%2F2 which are both rational numbers. Note: this is the same as part C, since any number (such as 2) is rational (ie 2=2%2F1) so any solution (that isn't irrational or complex) is rational


E)
When b^2-4ac is not equal to a perfect square (like 27), there are two irrational solutions because the square root of any number that is not a perfect square is irrational. Since an irrational number added to a rational number gives you an irrational number, the solutions will be irrational. For example, lets say we have:
%286%2B-sqrt%2827%29%29%2F2} which becomes %286%2Bsqrt%2827%29%29%2F2=8.59807621135331%0D%0A and %286-sqrt%2827%29%29%2F2=3.40192378864669%0D%0A which are both irrational (cannot be represented as a fraction)