Question

if alpha,beta,gamma are the zeros of the roots of the polynomial
${x}^{3} + 4x + 1$
then find
${( \alpha + \beta })^{ - 1} + {( \beta + \gamma )}^{ - 1} + {( \gamma + \alpha )}^{ \ - 1}$

​

Answer 1

Answer:

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Step-by-step explanation:

f(x)=2x

3

+x

2

−5x+2

f(

2

1

)=2(

3

1

)

3

+(

2

1

)

2

−5(

2

1

)+2

=

4

1

+

4

1

−

2

5

+2=0

f(1)=2(1)

3

+(1)

2

−5(1)+2=2+1−5+2=0,

f(−2)=2(−2)

3

+(−2)

5

2

(−2)+2=−16+4+10+2=0.

Let α=

2

1

,β=1, and γ=−2

Now, Sum of zeros =α+β+γ=

2

1

+1−2=−

2

1

Answer 2

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