Question

if alpha,beta are zeros of polynomial p(x)=x^2+x+1.find the value of 1/alpha+1/beta and alpha^2 +beta^2

Answer 1

Heya

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For a quadratic equation say

ax² + bx + c = 0
Alfa + Beta = -b/a
And
Alfa × Beta = c/a
=>

Here a = 1 , b = 1 And c = 1
Alfa + Beta = -1
And
Alfa × Beta = 1

=>

1)

1/Alfa + 1/ Beta =
{ Alfa + Beta } / Alfa × Beta

=>
1/Alfa + 1/Beta = -1

2)

Alfa² + Beta² =
{ Alfa + Beta }² - 2 Alfa × Beta

=>
Alfa² + Beta² = { -1 }² - 2 ( 1 )

=>
Alfa² + Beta² = -1