Question 3392
The number of real solutions to a quadratic equation is either 0, 1 or 2 depending on certain criteria. The easiest way to find the number is to look a something called the discriminant = {{{b^2 - 4ac}}}. The values for a, b and c are found in the equation itself. A quadratic equation always has the form {{{ax^2 + bx + c = 0}}}. In your example, a = 2, b = 4 and c = -4. The discriminant in the case would be {{{4^2 - 4*(2)*(-4)}}} since this value is greater than 0, we know there will be two real valued solutions. In fact they would be {{{(-4 + sqrt(4^2 - 4*(2)*(-4)))/(2*4)}}} and {{{(-4 - sqrt(4^2 - 4*(2)*(-4)))/(2*4)}}}. If the discriminant were zero, it would have one real solution and if it were less than zero, it would have no real valued solutions, but it would have two complex solutions.<br>
In short, this equation has two solutions.