Question

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

Answer 1

Answer:

sum of roots = 2a

product = a²-b

polynomial = x²-2ax+(a²-b) = 0 (Ans.)

Answer 2

Polynomial =  x²  - 2ax  + a² - b  if a + √b    &  a  -√b  are the zeroes of polynomial

Step-by-step explanation:

a + √b    &  a  -√b  are the zeroes of polynomial

Method 1 :

sum of roots = a + √b    +  a  -√b  = 2a

Product of Roots = (a + √b)(a  -√b) = a² - b

Polynomial =  x²  - 2ax  + a² - b

Method 2

f(x)  = (x - (a + √b))(x - (a - √b))

= x² - x(a + √b + a - √b)  +  (a + √b)(a - √b)

= x²  - 2ax  + a² - b

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