Question

Decide how many solutions the equation has. $$-2 x^{2}+4 x-2=0$$

Short answer

The quadratic equation \(-2 x^{2} + 4x - 2 = 0\) has exactly one real root.

Step-by-step solution

Identify a, b and c in the quadratic equation

In our quadratic equation, \(-2 x^{2} + 4x - 2 = 0\), the coefficients match up to the general form as follows: \(a = -2\), \(b = 4\), \(c = -2\).

Calculate the Discriminant

With the values of \(a\), \(b\), and \(c\), substitute them into the discriminant formula \(D = b^{2} - 4ac\). This gives \(D = (4)^{2} - 4*(-2)*(-2)\). Simplifying this gives: \(D = 16 - 16 = 0.\)

Determine the number of solutions

From the discriminant calculated, \(D = 0\), the quadratic equation has exactly one real root.