The standard form of a quadratic equation is: **ax**^{2}+bx+c = 0 where a, b and c are known values and a ≠0. Also, x is a real variable.

If the value of a is 0, then the equation will become a linear equation.

- A root of the equation f(x) = 0 is when the value of x makes f(x) = 0. We can say that x = a is the root of f(x) = 0. Here, f(a) is the value of the polynomial f(x) at x = 0 and is obtained by replacing x by a in f(x).
- If there is a quadratic equation
**ax**, then the roots of this equation will be:^{2}+ bx + c = 0 - In the above mentioned formula, b
^{2}- 4ac is the discriminant as it can discriminate between the possible types of solutions:

- When we have a positive value of b
^{2}- 4ac, then we will get two Real solutions - When the value of b
^{2}- 4ac is zero, then we will get only one Real solution - When we have a negative value of b
^{2}- 4ac, then we will get two Complex solutions (i.e. the answer will include imaginary numbers)

Let the roots of the equation ax^{2}+ bx + c be α and β.

- Then, the sum of the roots: α + β = -
- The product of the roots = α β =

- If p+ √q is a root of a quadratic equation, then its other root is p- √q
- When D ≥ 0, then ax
^{2}+ bx + c can be expressed as a product of two linear factors. - If α and βare the roots of ax
^{2}+ bx + c, then we can write it as: x^{2}- (α + β)x + α β = 0