Question

find the qudatic polynomial whose root is 3+√5and 3-√5​

Answer 1

Answer:

Let α=3+5  and β=35 

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=−16

Product of roots =ac=14 

⟹a=1,b=−6 and c=4 

Hence, the quadratic polynomial is x2−6x+4

Step-by-step explanation:

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Answer 2

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:

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