Sum and product of roots of quadratic equation

• The sum of the roots is equal to -b/a, and the product of the roots is equal to c/a, where a, b, and c are the coefficients of the quadratic equation in the standard form ax^2 + bx + c = 0. Several examples are worked out applying these formulas.
• To find the roots when the discriminant is negative or zero, use the quadratic formula with i as an imaginary unit.
• If the discriminant D is negative, then there are no real solutions; if it is zero, then one root is repeated twice; and if it is positive, then two distinct real roots exist.
• When finding the square root of a complex number, take the principal value between 0 and 2π radians.
• When finding the roots using the quadratic formula, be careful not to confuse x1 and x2.
• In the case of a repeated root, the quadratic formula can be used to calculate the multiplicity of that root.
• A quadratic function has at most two x-intercepts, which correspond to its zeros or roots.
• Factored forms include perfect squares, difference of squares, trinomials, and special products like (ax+b)(cx+d).
• The graph of a quadratic function always intersects both axes.
• The vertex form of a parabola is y = a(x - h)^2 + k, where (h,k) is the vertex and a determines whether the parabola opens upwards or downwards.
• The axis of symmetry passes through the vertex and bisects the line segment connecting the zeros of the quadratic function.