Question

$\alpha + \beta \: \: are \: the \: roots \: of \: {x}^{2} + 2x + c = 0. \: if \: { \alpha }^{3} + { \beta }^{3} = 4. \: then \: find \: the \: value \: of \: c$
Please give the answer fast guys...​

Answer 1

Answer:

c = 2

Step-by-step explanation:

By theory of equations,

α + β = -2                     (sum of roots is equal to -b/a )

Given,

α³ + β³ = 4

⇒ (α + β).(α² - αβ + β²) = 4                  (a³ + b³ formula)

⇒ -2{(α+β)² - 3αβ} = 4

⇒ 4 - 3αβ = -2

⇒ αβ = 2

We know that αβ = c/a

Here, a = 1

⇒ αβ = c = 2

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