Question

if alpha beta gamma are the roots of the equation 2 x cube + x square + X + 1 is equal to zero then find the value of summation 1 by Alpha square​

Answer 1

Answer:

Correct option is

A

−

4

15

Given equation 2x

3

−3x

2

+6x+1=0,

Sum of roots:

α+β+γ=

2

3

,

Product of roots:

αβγ=

2

−1

,

Sum of roots taken 2 at a time:

Σαβ=

2

6

=3

Now, we know that

(α+β+γ)

2

=α

2

+β

2

+γ

2

+2(αβ+βγ+γα)

Re-arranging, we get

α

2

+β

2

+γ

2

=(α+β+γ)

2

−2(Σαβ)

α

2

+β

2

+γ

2

=(

2

3

)

2

−2×3=

4

9

−6=−

4

15