Question

find the discriminant of the quadratic equation and give the number and type of solutions of the equation.\\(x^2 - 2x - 1 = 0\\)\
the discriminant is select\
so there is/ are select (options for discriminant: 8, 0, 12, -4)\
question 2

Explanation:

Step1: Recall discriminant formula

For a quadratic equation \(ax^2 + bx + c = 0\), the discriminant \(D\) is given by \(D = b^2 - 4ac\).

Step2: Identify coefficients

In the equation \(x^2 - 2x - 1 = 0\), we have \(a = 1\), \(b = -2\), and \(c = -1\).

Step3: Calculate discriminant

Substitute the values into the formula: \(D = (-2)^2 - 4(1)(-1)\)
First, calculate \((-2)^2 = 4\). Then, calculate \(4(1)(-1) = -4\). Now, \(D = 4 - (-4) = 4 + 4 = 8\).

Answer:

The discriminant is 8. So there are two distinct real solutions (since the discriminant is positive and not a perfect square, but for the discriminant value, the answer is 8).