A quadratic equation is a polynomial equation of the second degree, meaning it contains at least one variable that is squared but no variables that are raised to a higher power. The general form of a quadratic equation in one variable (usually represented by x) is:
�
�
2
+
�
�
+
�
=
0
,
ax
2
+bx+c=0,
where a, b, and c are constants (numbers) and a is not equal to zero. The term ax^2 is called the quadratic term, bx is the linear term, and c is the constant term.
To solve a quadratic equation, we can use the quadratic formula:
�
=
−
�
±
�
2
−
4
�
�
2
�
.
x=
2a
−b±
b
2
−4ac
.
This formula gives us the solutions (values of x) for any quadratic equation in the standard form. The expression under the square root, b^2 - 4ac, is called the discriminant of the quadratic equation.
The discriminant can tell us a lot about the nature of the solutions of the quadratic equation. If the discriminant is positive, then the quadratic equation has two distinct real solutions. If the discriminant is zero, then the quadratic equation has one real solution, called a double root or a repeated root. If the discriminant is negative, then the quadratic equation has two complex (non-real) solutions, which are conjugates of each other.