SOLUTION: For what value of 2x^2-3x+c=0 have one and only one real root?

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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