Question

Find quadratic polynomial whose zeroes are3+√5/2
,3-√5/2

Answer 1

Answer:

k(x2^ -6x +4)

Step-by-step explanation:

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

or...

zeroes = 3+root5 and 3-root5

product of zeroes= (3+root5)(3-root5)

= 9-5

=4

sum of zeroes=3+root5 + 3-root5

=6

we know p(x) = k(x2^ - sum of zeroes (x) + product of zeroes

= k(x2^ -6x +4)