Quadratic Equations

posted on: 16 May, 2012 | updated on: 14 Sep, 2012

The polynomial which can be expressed in the form of ax² + bx + c = 0, then we say that the equation is in the form of quadratic polynomial. Here we say that a, b, c are the real Numbers and we must remember that a <> 0, since if we have a = 0, the equation will convert into a linear equation in place of the quadratic equation. If we say that alpha (α) and beta (β) are the two roots of the Quadratic Equation and their sum of the root i.e. α + β is written as = - coefficient of ‘x’ / coefficient of x².
Also the products of the roots is written as α * β = c/a,

Now in case the roots of the equation are known, then we can form the quadratic equation using the following formula:
x² – sum of roots * x + product of roots = 0
We can find the solution of the quadratic equations by Factorization, by completing the squares and making them the perfect squares and it is also done even by the quadratic formula.

Once we learn to use the formula of the quadratic roots and to find the value of the determinants, and the nature of roots can also be known.
Now let us see that α and β are the roots of the quadratic equation, then it means that if we put the value of α or β in the given equation, then it satisfies the given equation.
D = b² – 4 * a * c is the formula which helps to analyze the types of roots of the equation. If D = 0, then roots are real and equal, if D> 0, then roots are unequal and real, if D< 0, then roots are imaginary.

Topics Covered in Quadratic Equations

Quadratic Formula

posted on: 14 Jul, 2012 | updated on: 13 Sep, 2012

An equation whose highest degree is equals to 2 is known as Quadratic Equation. In other words an equation whose highest power is a Square is said to be quadratic equation. Quadratic equation can be written as: ax² + bx + c = 0 and Quadratic Formula is given by:
⇨ x = - b + √ (b² – 4ac) / 2a, its alternate form also given by:
⇨ x = 2c / -b +√ (b² – 4ac).

Now w...Read More

Square Root Property

posted on: 16 Jul, 2012 | updated on: 14 Sep, 2012

Square root property can be explained as a Square root which is the mathematical reverse of a squared exponent. It also says that squaring of a positive or a negative number will be equals to a positive number. Square root property states that if a² = b then a = √b or a = -√b, which can also be written as, a = ±√b. Here we will have two values possibly. Both values ...Read More

Completing the Square

posted on: 16 Jul, 2012 | updated on: 06 Sep, 2012

We are very much aware of formula for Square of addition or subtraction of two Numbers which can be given as:

(a + b) ² = a² + b² + 2ab and
(a - b) ² = a² + b² - 2ab,
When you have a Quadratic Equation of form ax² + bx + c which is not possible to be factorized, you can use technique called completing the square. To complete the square means creating a polyno...Read More

Applications of Quadratic Equations

posted on: 16 Jul, 2012 | updated on: 06 Sep, 2012

Quadratic equations means an equation which is written in form of ax² + bx + c = 0. In real life we come across many practical problems which are related to applications of our life. If we know area of R...Read More

Define Quadratic Equation

posted on: 14 Jun, 2012 | updated on: 14 Sep, 2012

We can Define Quadratic Equations as polynomial equations in which highest power of variable is 2, thats why it is also called second degree equation. General form of Quadratic Equation is ax² + bx + c = 0 , here 'x' is a variable and a, b, c are constants they are also called as quadratic coefficient, and highest power is two, in this equation there is a condi...Read More

Quadratic Equations by Factoring

posted on: 07 Jul, 2012 | updated on: 06 Sep, 2012

A Quadratic Equation can be defined as polynomial equation with degree two or we can say it is second degree polynomial equation. General form of quadratic equation is px² + qx + r = 0, here 'x' is a variable whise value is unknown and p, q, and r are constants where 'p' can not be equals to 0. That means p ≠ 0. Constants p, q, and r are called as qua...Read More