Question

If 3+√5 is one root then find the quadratic equation

Answer 1

hi mate,

solution:

take conjugate pair of 3+√5 is 3 - √5

Given ->

3 - √5 and 3 + √5 are zeros of a polynomial

let p(x) be required polynomial

====> x - (3 + √5) and x - (3 - √5) are factors of p(x)

====> [x - (3 + √5)] [x - (3 - √5) is required polynomial

= [x - 3 - √5] [x - 3 + √5]

= x - 3x + √5x - 3x + 9 - 3 √5 - √5x

+ 3 √5 -5

= x² - 6x + 4

i hope it helps you.