Question

Find quadriatic polynomial whose zeros are 4+route5and4-route5

Answer 1

Answer:

x²-8x+11 = 0

Step-by-step explanation:

Let the unknown polynomial be

ax² + bx + c = 0

The roots of the unknown polynomial is given to us as (4+√5) and (4-√5)

Sum of roots = 4+√5+4-√5 = 8 = -b/a

Product of roots = (4+√5)(4-√5) = 16 - 5 = 11 = c/a

By comparing, we identify that

a = 1

b = -8

c = 11

So the polynomial is

x² - 8x + 11 = 0