Question

find a quadratic polynomial whose zeroes are 1/2+2 root 3 and 1/2-2 root 3

Answer 1

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

Step-by-step explanation:

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