BCA PART A 2. Solve Quadratic Equations

A quadratic equation is a second-order polynomial equation in a single variable, usually written in the standard form:

$�{�}^2+��+�=0$

where $�$ represents the variable, and $�$, $�$, and $�$ are constants with $�\mathrm{\ne }0$. The coefficients $�$, $�$, and $�$ determine the shape and position of the parabola formed by the graph of the quadratic equation.

The solutions to the quadratic equation, also known as the roots, can be found using the quadratic formula:

$�=\frac{-�\pm \sqrt{{�}^2-4��}}{2�}$

The term inside the square root, ${�}^2-4��$, is called the discriminant. The nature of the roots is determined by the value of the discriminant:

• If the discriminant is positive (${�}^2-4��>0$), the equation has two distinct real roots.
• If the discriminant is zero (${�}^2-4��=0$), the equation has one real root (a repeated root).
• If the discriminant is negative (${�}^2-4��<0$), the equation has two complex conjugate roots.

Quadratic equations often arise in various mathematical and scientific contexts, and they are used to model a wide range of physical phenomena. The graph of a quadratic equation is a parabola, and understanding its properties is essential in algebra and calculus.