QUADRATIC EQUATION FROM ROOTS

In this page we are going to see how to find quadratic equation from roots.

General form of quadratic equation with roots α and β is

x² - (α + β) x + αβ = 0.

  • α + β = Sum of roots
  • α β = Product of roots

Example 1:

Find the quadratic equation with roots -4 and 3.

Solution:

Here two roots are -4 and 3

α = -4

β = 3

General form of any quadratic equation x² - (α + β) x + αβ = 0

Sum of roots (α + β) = - 4 + 3

                            = -1

Product of roots (α β) = - 4 (3)

                              = -12

Now let us write the quadratic equation with sum and product of roots

x² - (-1) x + (-12) = 0

x² +  x - 12 = 0


Example 2:

Find the quadratic equation with roots 1/4 and -1.

Solution:

Here two roots are 1/4 and -1

α = 1/4

β = -1

General form of any quadratic equation x² - (α + β) x + αβ = 0

Sum of roots (α + β) = (1/4) + (-1)

                            = (1 - 4)/4

                            = -3/4

Product of roots (α β) = (1/4) (-1)

                              = -1/4

Now let us write the quadratic equation with sum and product of roots

x² - (-3/4) x + (-1/4) = 0

x² + 3 x/4 - 1/4 = 0

(4x² + 3 x - 1)/4 = 0

4x² + 3 x - 1 = 0 


Example 3:

Find the quadratic equation with roots √3 and 2.

Solution:

Here two roots are √3 and 2

α = √3

β = 2

General form of any quadratic equation x² - (α + β) x + αβ = 0

Sum of roots (α + β) = √3 + 2

Product of roots (α β) = √3(2)

                              = 2√3

Now let us write the quadratic equation with sum and product of roots

x² - (√3 + 2) x + (2√3) = 0

x² - (√3 + 2) x + 2√3 = 0

x² +  x - 12 = 0

This is the method of framing quadratic equation from root.


Quote on Mathematics

“Mathematics, without this we can do nothing in our life. Each and everything around us is math.

Math is not only solving problems and finding solutions and it is also doing many things in our day to day life.  They are: 

It subtracts sadness and adds happiness in our life.    

It divides sorrow and multiplies forgiveness and love.

Some people would not be able accept that the subject Math is easy to understand. That is because; they are unable to realize how the life is complicated. The problems in the subject Math are easier to solve than the problems in our real life. When we people are able to solve all the problems in the complicated life, why can we not solve the simple math problems?

Many people think that the subject math is always complicated and it exists to make things from simple to complicate. But the real existence of the subject math is to make things from complicate to simple.”




Quadratic Equation From Roots to Worksheets