Question

If albha, beta, gama , are zeros of polynomial x cube - 5 x square + 2 x -1 than find alpha square + beta square + gama square

Answer 1

Answer:

α²+β²+γ²=21

Step-by-step explanation:

given α,β,γ are the roots of x³-5x²+2x-1

let x³coefficient be a  ⇒ a=1

    x² coefficient be b  ⇒ b=-5

    x coefficient be c    ⇒ c=2

   

sum of the roots α+β+γ=-b/a=-(-5)/1

                           α+β+γ=5.............................equation 1

αβ+βγ+γα=c/a=2/1

⇒αβ+βγ+γα=2..................................................equation 2

we know that ,  (α+β+γ)²=α²+β²+γ²+2(αβ+βγ+γα)

from equations 1 and 2 we get

5²=α²+β²+γ²+2(2)

25=α²+β²+γ²+4

α²+β²+γ²=21

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