Question

If a+√b and a-√b are the zeroes of a polynomial, then find the polynomial.

Answer 1

Answer:

Given, the zeroes of the polynomial are a+√b and a-√b

Step-by-step explanation:

we know know that,

α=a+√b

β=a-√b

sum of the zeroes= a+√b+(a-√b)

                           =a+a+√b-√b

                            =2a

product of the zeroes=(a+√b)(a-√b)

                                   =a^2-a√b+a√b-√b^2

                                    =a^2-b

 quadratic polynomial is

k[x^2-(sum of the zeroes)x+product of the zeroes], k is a scalar

k[x^2-(2a)x+a^2-b], k is a scalar

k[(x^2-2ax+a^2)-b], k is a scalar

k[(x-a)^2-b], k is a scalar

∴ the polynomial is

       =(x-a)^2-b