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: