Question

find the quadratic equation (5+2√3)and(5-2√3)

Answer 1

equation is given by
x square - (sum of roots )x + product of roots = 0
hence x sq - 10x + 13= 0

Answer 2

hello users ...

Solution:-
we know that:
For a quadratic equation :ax² + bx + c = 0 ........(1.) :

Sum of roots ( α + β ) = - b / a
And
product of roots (αβ ) = c / a 

where, α and β are the roots of equation.

Here,
Given ;
two roots 
α = ( 5 + 2√3 ) 
β = ( 5 - 2√3 ) 

Now,
Sum of roots (α + β) = - b / a 

=> - b / a =  ( 5 + 2√3 )+( 5 - 2√3 ) 

=> - b / a = ( 5 + 2√3 + 5 - 2√3 ) 

=> - b / a = 10

=>   b / a = -10 / 1

Now,
product of roots (αβ) = c / a 

=> c / a =  ( 5 + 2√3 )×( 5 - 2√3 )

=> c / a = [ 5² - (2√3)² ]  
using ..
 (a+b)(a-b) = (a² - b²) 

=> c / a = 25 - 12 = 13 

=> c / a = 13 / 1 

Comparing Above ...
Here,
a = 1 , b = -10 and c = 13 

Putting values in equation (1.)

=> x² - 10 x + 13 = 0  is the required quadratic equation. 

Hope it helps :)