Graph the quadratic. If the graphed curve does not cross the X axis, the quadratic has no real roots. If this quadratic is part of a real world problem, the problem has no solution. If there are only complex solutions, there will be two and they will be complex conjunctions. This means that one will be in the form a + bi and the other will be a - bi.
Discover that a quadratic has two real roots when the parabola crosses the X axis in two places. The graph of quadratics will always be parabolas. The equation will look like aX^2 + bX + c = 0. If "a" is greater than zero, the parabola opens upward and the vertex of the parabola represents a minimum value for the quadratic. If the quadratic opens upward and has two real roots the minimum value will have a negative Y value. If "a" is less than zero, the parabola opens downward and the vertex of the parabola represents a maximum value for the quadratic. If it also has two real roots, the Y value of the vertex will be positive. The points where the curve crosses the X axis mark the roots of the quadratic.
Understand that there is a multiple root when the parabola just touches the X axis at one point. Multiple roots mean that there are two roots, but they are equal. An example of this is the quadratic x^2 - 6X + 9 = 0. This is a square polynomial so the factors are equal: (X - 3)(X - 3) = x^2 - 6X + 9 = 0. There are two roots, but they are both 3. The point where the vertex touches the X axis is (3, 0).