Question

Find a quadratic polynomial whose zeros are 3 plus root 5 /5 And 3-root5/5

Answer 1

Let the 2 zeroes be α and β.
Given :
One zero ( α) = 3+√5/5 , other zero (β) = 3- √5/5
Sum of the zeroes = (α + β)
Sum of the zeroes =[3+√5/5 + 3 - √5/5]
Sum of the zeroes = 3 +3 = 6

Product of zeroes= αβ
Product of zeroes= [(3+√5/5 )× (3 - √5/5)]
Product of zeroes = (3)² - (√5/5)²
[(a+b)(a-b) = a² - b² ]
= 9 - 5/25
= 9 - ⅕
=( 45 - 1)/5
= 44/5
Product of zeroes = 44/5

The quadratic polynomial with α and β as zeroes is k [ x²− (α + β)x + (αβ)], where k is a non zero real Number.

Hence the quadratic polynomial is:
k [x² − (6)x + 44/5]
=k/5[ 5x² − 30x + 44]
= 5x² −30x + 44                               [k = 5]

Hence, the quadratic polynomial is 5x² −30x + 44

HOPE THIS WILL HELP YOU...