Question

Find a quadratic polynomial whose zeroes are 5+root2 and 5-root2

Answer 1

Hi Sarvadnay,
here
let alpha be 5 + root 2 and beta be 5 - root 2
thereby using standard quadratic equation form
X2(Squared) - (2alpha*beta)x + alpha*beta
after calculation
we get,

X2(squared) -10x +23 is required quadriatic equation

Answer 2

hello users .......

we have given that :
zeros of quadratic equation are 5 + √2 and 5 - √2

we have to find the quadratic equation ;

solution :-
we know that :
for a quadratic equation :ax² + bx + c = 0 

sum of roots (zeros ) of quadratic equation = -b/a 
and 
product of roots (zeros) = c/a 

here ,
let α and β are the roots of equation 

=> sum of roots = -b / a = ( 5 + √2 ) + (5 - √2 )

=> - b / a = 10 /1
 
=>b / a = -10 / 1......(1) 

and 
product of roots = c / a =  ( 5 + √2 ) (5 - √2 ) 
= 25 - 5√2 + 5√2 -2 
= 25 - 2 = 23 
=> c / a = 23 / 1 .......(2) 

from (1) and (2) 
a = 1 , b = -10 and c = 23 

hence
quadratic equation is ax² + bx + c = 0 
= x² -10x +23 = 0 answer 

☆☆ hope it helps ☆☆