Questions on Algebra: Quadratic Equation answered by real tutors!

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Start with the discriminant formula


Plug in , and


Multiply 4 and 2 to get 8


Multiply 8 and 9 to get 72


So we'll use the equation to solve the following:

1) "find the values of k for which the quadratic has one real solution"


If a quadratic has one real solution, then the discriminant is equal to zero. So this means that


Start with the previous equation


Plug in


Add 72 to both sides


Take the square root of both sides


or Break up the "plus/minus"


or Simplify the square root


So if or , then the discriminant is equal to zero. This means that the equation or only has one real solution.

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2) "find the values of k for which the quadratic no real solutions"


If a quadratic has no real solutions, this means that the discriminant is less than zero. In other words,


Go back to the previous equation


Since , this means that the right side is less than zero

Add 72 to both sides


Take the square root of both sides


or Break up the "plus/minus"


or Simplify the square root


Recombine the two inequalities to form one compound inequality

So if "k" is in between and , then the discriminant is less than zero. This means that if "k" is in between and , then the quadratic will have no solutions