Let \(a\) be a real number for which there exists a unique value of \(b\) such that the quadratic equation \(x^2 + 2bx + (a-b) = 0\) has one real solution. Find \(a\).
Use the quadratic formula
The bit under the square root will have to be 0 if there is to be only 1 root.
The bit under the square root is called the discriminant because it discriminates between different kinds of roots.
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