The quadratic formula is used to find the solutions (roots) of a quadratic equation of the form ax2+bx+c=0ax^2+bx+c=0ax2+bx+c=0, where a≠0a\neq 0a=0. The formula is:

x=−b±b2−4ac2ax=\frac{-b\pm \sqrt{b^2-4ac}}{2a}x=2a−b±b2−4ac​​

Here, the symbol ±\pm ± means there are generally two solutions: one with the plus sign and one with the minus sign, given by

x1=−b+b2−4ac2a,x2=−b−b2−4ac2a.x_1=\frac{-b+\sqrt{b^2-4ac}}{2a},\quad x_2=\frac{-b-\sqrt{b^2-4ac}}{2a}.x1​=2a−b+b2−4ac​​,x2​=2a−b−b2−4ac​​.

The term under the square root, Δ=b2−4ac\Delta =b^2-4acΔ=b2−4ac, is called the discriminant. It determines the nature of the roots:

• If Δ>0\Delta >0Δ>0, there are two distinct real roots.
• If Δ=0\Delta =0Δ=0, there is one repeated real root.
• If Δ<0\Delta <0Δ<0, there are two complex conjugate roots.

This formula provides a direct way to solve any quadratic equation and also gives information about the graph of the quadratic function, such as the xxx- intercepts of its parabola and the axis of symmetry.