Question

if alpha + beta equal to 4 and Alpha Cube + beta cube equal to 44 then the polynomial having zeroes
alpha, beta is​

Answer 1

Answer:

α = 0.47 , β = 3.53

        OR

α = 3.53  , β = 0.47

Step-by-step explanation:

α+β = 4

α = 4-β

α³+β³ = 44

(α+β)³ = α³+β³+3αβ*(α+β)

4³ = 44 + 3αβ*4

64-44 = 12αβ

20 = 12αβ

5 = 3 αβ

5 = 3*(4-β)β

5 = 12β-3β²

3β²-12β+5 = 0

a= 3

b = -12

c = 5

d = b²-4ac

d = -12²-4*3*5

d = 144-60

d = 84

β = (-b±√d)/2a

β = (12 ± √84)/2*3

β = (12±9.1651513899)/6

β =( 12±9.165)/6

β = 21.165/6  ║  2.835/6

β = 3.5275    ║  0.4725

if β = 3.5275 = 3.53

α = 4-β = 4-3.53 = 0.47

if β = 0.4725

α = 4-β = 4-0.47 = 3.53

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