Question 515532: For what value of 2x^2-3x+c=0 have one and only one real root?
Answer by MathLover1(20850)   (Show Source):
You can put this solution on YOUR website! So, for what value of c will  have one and only one real root? To answer this question, let's think about the quadratic formula:
Specifically take note of the  . What's inside of this radical is known as the determinant, because it determines how many roots there will be.
 this  is  , then there are   solutions. This is because you can't take the square root of a negative number without using imaginary numbers. Therefore, a negative determinant implies no real roots.
this is  , then there are  solutions. This is because of the ± in the quadratic formula.
the happened to be  , then you'd have   : one you would have to add the , and the other you would have to subtract the .
the is  , then there is   solution. This is because + or - zero leaves the quadratic formula unchanged. In summary:
One real solution: 
Two real solutions:
No real solutions: 
So let's solve to see when the determinant equals zero, so there will be only one real root. We will use the a, b, and c values from the equation you provided earlier.
Let's set the determinant equal to zero, and then substitute the known values:
 must be equal to  for the equation to have one and only one real root.
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