Question

find the quadratic polynomial whose roots are 3+ root3 and 3- root3​

Answer 1

Step-by-step explanation:

Given :-

3+ root3 and 3- rroot3

To find :-

Find the quadratic polynomial whose roots are

3+ √3 and 3- √3 ?

Solution:-

Given roots are 3+ √3 and 3- √3

Let α = 3+√3

Let β = 3-√3

α + β = 3+√3+3-√3 = 3+3 = 6

α β = (3+√3)(3-√3)

It is in the form of (a+b)(a-b)

Where a = 3 and b =√3

(a+b)(a-b)=a^2-b^2

(3+√3)(3-√3) = 3^2-(√3)^2

=> 9-3

=> 6

We know that

If α and β are the roots ,then the Quadratic equation is x^2-(α +β)x+αβ = 0

=> x^2-(6)x+6 = 0

=> x^2-6x+6 = 0

Answer:-

The required quardratic equation is x^2-6x+6 = 0

Used formulae:-

• If α and β are the roots ,then the Quadratic equation is x^2-(α +β)x+αβ = 0