Question

if alpha and beta are the zeroes of the polynomial x^2+x+1 then find 1/ alpha +1/beta
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Answer 1

Answer:

Answer:

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${x}^{2} + x + 1 = 0$

On comparing this Eq with

$a {x}^{2} + bx + c = 0$

We get,

a = 1 , b = 1 , c = 1

So,

$\alpha + \beta = \frac{ - b}{a} = \frac{ - 1}{1} = - 1 \\ \alpha \beta = \frac{c}{a} = \frac{1}{1} = 0 \\ \frac{1}{ \alpha } + \frac{1}{ \beta } = \frac{ \beta + \alpha }{ \alpha \beta } = \frac{ \alpha + \beta }{ \alpha \beta } = \frac{1}{1} = 1$

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Answer 2

Explanation:

Aloha !

Given equation ,

x²+X+1=0

The general equation of linear polynomial is

ax²+by+c=0

Where,

a=1

b=1

c=1

Sum of roots = -b/a=-1

product of roots =c/a=1

Now,

1/à+1/ß=à+ß/àß=1

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