Form a quadratic polynomial whose one zero is 3-√5 . . .

Question : Form a quadratic polynomial whose one zero is 3-√5 and the product of zeroes is 4.

Doubt by Mehak

Solution :

α = 3-√5 
αβ = 4

(3-√5)β=4

β = 3+√5

α+β = 3-√5+3+√5

α+β = 3+3

α+β = 6

Required quadratic polynomial

=k(x²-(α+β)x+αβ]
=k(x²-6x+4)

where k is a constant.