Learn Real Roots

In this article we are going to learn about real roots .Roots are the value of the variable that satiafies the given equation.It is also called as sollutions of the equations.The solution may be positive,negative or imaginary numbers.Whenthe roots are real values then its called as real roots. An equation which contains more than one terms are squared but no higher power in terms, having the syntax, ax2+bx+c where a represents the numerical coefficient of x2, b represents the numerical coefficient of x, and c represents the constant term

Example: 4x2+7x+18
Identify the Real Roots in Quadratic Equation

A quadratic equation is in the form of ax2+bx+c,

First we need to find the discernment d = b2- 4ac

If d > 0, the roots are real roots and unequal

If d = 0, the roots are real and equal

If d< 0, the roots are imaginary.
Example of Real Roots

Below you can see the example of real roots -

Example1: Solve the quadratic equation

x2+21x+20

Solution:

The equation is in the form of  ax2+bx+c

Where a=1 and b= 21 and c= 20

Find the discernment d = b2- 4ac

d = (21)2 - 4* 1* 20

d = 441 -80

d = 361 > 0

If d > 0, the roots are real roots and unequal

To find the roots, the following steps are used

Step 1: Multiply the coefficient of x2 and the constant term,

1*20 = 20 (product term)

Step 2: Find the factors for the product term

20--- > 1*20 = 20 (factors are 1 and 20)

20 --- > 1 + 20 = 21 (21 is equal to the coefficient of x)

Step 3: Separate the coefficient of x

x2 + 21x+20

x2 + x + 20x + 20

Step 4: The common term x for the first two terms and 20 for the next two terms are taking outside

x(x + 1) + 20 (x + 1)

(x + 1) (x + 20)

Set this value equal to zero

(x +1) = 0; x = -1

(x+20) = 0; x =-20

Roots of the quadratic equations x =-1 and x= -20

Example2: Solve the quadratic equation

x2+4x+4

Solution:

The equation is in the form of  ax2+bx+c

Where a=1 and b= 4 and c= 4

Find the discernment d = b2- 4ac

d = (4)2 - 4* 1* 4

d = 16 -16

d = 0

If d = 0, the roots are real roots and equal

To find the roots, the following steps are used

Step 1: Multiply the coefficient of x2 and the constant term,

1*4 = 4 (product term)

Step 2: Find the factors for the product term

4--- > 2 * 2 = 4 (factors are 2 and 2)

4 --- > 2 + 2 = 4 (4 is equal to the coefficient of x)

Step 3: Separate the coefficient of x

x2 + 4x+4

x2 + 2x + 2x + 4

Step 4: The common term x for the first two terms and 2 for the next two terms are taking outside

x(x + 2) + 2 (x + 2)

(x + 2) (x + 2)

Set this value equal to zero

(x + 2) = 0; x = -2

(x + 2) = 0; x =-2

Roots of the quadratic equations x =-2.