Question

if alpha and beta are the two zeros of polynomial x2+x+1 then find A2+B2

Answer 1

The answer is given below :

The given polynomial is (x² + x + 1).

Since, α and β are the roots of the polynomial, we get

α + β = (- 1)/1

⇒ α + β = - 1 .....(i)

and

αβ = 1/1

⇒ αβ = 1 .....(ii)

Now,

α² + β²

= (α + β)² - 2αβ

= (- 1)² - (2 × 1)

= 1 - 2

= - 1

Thank you for your question.

Answer 2

HEY YOUR ANSWER IS .....

It is given that alpha and beta are the zeros of polynomial x^2 + x + 1 .....

So ,

alpha+beta=-b/a =-1/1 = -1

And.....

alpha×beta=c/a =1/1 = 1

Comparing with p(x) = x^2+x+1

Here , a = 1 , b = 1 and c = 1 .

So , (a+b)^2 = a^2 +2ab+b^2

So , 4 = 1 +2+1

So , 4 = 4 .

So , LHS= RHS .