Question

find the quadratic polynomial with zero 3 + root 2 and 3 minus root

Answer 1

So  we have , roots = +√3  and -√3  as the alpha and beta
now  sum of roots , i.e., alpha + beta =  -√3  +√3 
                                                           =     0
And product of roots , i.e., alpha * beta=   +√3  * -√3
                                                                =  -3
formula of forming quadratic equation is = x^2 -(sum of roots)x + product of roots
  
so definitely, we get our quadratic equation:
x^2 - 0x +(-3)
  which becomes,
x^2- 3 ( required answer).

Answer 2

Hiii friend,

(3+✓2) and (3-✓2) are the zeros of the polynomial.

Sum of zeros = (Alpha+Beta) = (3+✓2)+(3-✓2) = 6

Product of zeros = (Alpha ×Beta) = (3+✓2)(3-✓2) = (3)² - (✓2)² = 9-2 = 7

Therefore,

QUADRATIC POLYNOMIAL = X²-(Alpha+Beta)+Alpha × Beta

=> X²-6X+7.

Hence,

Quadratic polynomial = X²-6X+7.


HOPE IT WILL HELP YOU.... :-)