Question

Find the quadratic polynomial whose zeroes are 3+√5 and 3-√5

Answer 1

The quadratic polynomial with α and β as zeroes is x2�− (α + β)x + (αβ)
Given zeroes of the polynomial are 3+√5�and 3-√5
Hence the quadratic polynomial is:
x2�− (3+√5 + 3 −√5)x + (3+√5)(3 −√5)
= x2�− 6x + (9 −5)
= x2�− 6x + 4
Thus the quadratic polynomial is ( x2�− 6x + 4