# HOW TO FIND POLYNOMIAL EQUATION WITH GIVEN ROOTS

## About "How to find polynomial equation with given roots"

How to find polynomial equation with given roots :

We have to consider the roots as α and β. From this roots we can find the quadratic polynomial.

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 we have to apply this sum and product of roots in the general form of quadratic equation.

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 we have to apply this sum and product of roots in the general form of quadratic equation.

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 :

The given 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 we have to apply this sum and product of roots in the general form of quadratic equation.

x² - (√3 + 2) x + (2√3) = 0

x² - (√3 + 2) x + 2√3 = 0

x² +  x - 12 = 0

After having gone through the stuff given above, we hope that the students would have understood "How to find polynomial equation with given roots".

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