Question

if sigma alpha=2/3, sigma alpha into bita =4/3 and sigma alpha into bita into gama =8/3 then the equation whose roots are alpha,bita,gama is​

Answer 1

Answer:

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

Step-by-step explanation:

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