Question

Find a quadratic polynomial whose zeroes are 5 + √3 5 − √3.​

Answer 1

Answer:

Find a quadratic polynomial whose zeros are 3+  

5

​  

 and 3−  

5

​  

 

Answer

Let α=3+  

5

​  

  and β=3  

5

​  

 

Sum of zeros =α+β=3+  

5

​  

+3−  

5

​  

=6  

Product of zeros =αβ=(3+  

5

​  

)(3−  

5

​  

)=9−5=4  

Also, Sum of roots =  

a

−b

​  

=−  

1

6

​  

 

Product of roots =  

a

c

​  

=  

1

4

​  

 

⟹a=1,b=−6 and c=4  

Hence, the quadratic polynomial is x  

2

−6x+4

Step-by-step explanation: