Solving Quadratic Equations

A quadratic equation is a polynomial  equation, with one unknown in which the highest power of the unknown is 2.  Also called second degree equation in the unknown. The general or standard form of a quadratic equation is:

ax2 + bx + c + 0, where a,b,c are constants, and the number a ≠ 0. cannot equal to zero.


4x2 + 6x -10 = 0

5x2 - 7x + 21 = 0

3x2 = 15

All of the above equations are quadratic equations .

Thus, 4x2 + 6x - 10 = 0 is in standard form. Here, a = 4, b = 6, and c = - 10

To solve a quadratic equation is to determine the values of the unknown which will satisfy the equation. The numbers that will satisfy a quadratic equations are called: solutions or roots. In the event, that the solutions or roots of a quadratic equation are:

1) Real numbers like 3, - 5, √3, 1.65...then the roots are said to be real.

2) If the equation is satisfied by numbers like √-3, √-5, √-5.25..., the roots are said to be imaginary. Such solutions belong to the complex number system.

There are other methods for solving quadratic equations. They are:

Standard Form of Quadratic Equation

Solving Quadratic Equations by factoring.

Solving incomplete Quadratic Equations.

Solving Quadratic Equation by completing the Square.

Solving a Quadratic Equation by Quadratic Formula.