Question

6. Find a quadratic polynomial whose zeroes are 12 + 2√3 and 12 - 2√3.

Answer 1

Answer:

Step-by-step explanation:

Let the zeroes of the quadratic polynomial be α=1+2  

3

​  

,β=1−2  

3

​  

 

Then, a+β=1+2  

3

​  

+1−2  

3

​  

=2

αβ=(1+2  

3

​  

)×(1−2  

3

​  

)=1−12=−11

Sum of zeroes =a+β=2 Product of zeroes =αβ=−11

Then, the quadratic polynomial=x  

2

−( sum of zeroes )x+ product of zeroes =x  

2

−(2)x+(−11)

=x  

2

−2x−11