Question 1

What is the quadratic formula?

Accepted Answer

The quadratic formula solves ax^2 + bx + c = 0: x = (-b +/- sqrt(b^2 - 4ac)) / (2a). It always works for quadratic equations, giving two solutions (which may be equal or complex numbers).

Question 2

What is the discriminant?

Accepted Answer

The discriminant (b^2 - 4ac) determines the nature of solutions: positive = two real solutions, zero = one repeated solution, negative = two complex conjugate solutions. It tells you about the parabola and x-axis intersection.

Question 3

When does a quadratic have no real solutions?

Accepted Answer

When the discriminant is negative (b^2 - 4ac < 0), the parabola does not cross the x-axis and the equation has two complex solutions. Example: x^2 + 1 = 0 has solutions x = i and x = -i.

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