[tex] \alpha + \beta \: \: are \: the \: roots \: of \: {x}^{2} + 2x + c = 0. \: if \: { \alpha }^{3} + { \beta }^{3} = 4. \: then \: find \: the \: value \: of \: c[/tex]
Please give the answer fast guys...
Share
[tex] \alpha + \beta \: \: are \: the \: roots \: of \: {x}^{2} + 2x + c = 0. \: if \: { \alpha }^{3} + { \beta }^{3} = 4. \: then \: find \: the \: value \: of \: c[/tex]
Please give the answer fast guys...
Sign Up to our social questions and Answers Engine to ask questions, answer people’s questions, and connect with other people.
Login to our social questions & Answers Engine to ask questions answer people’s questions & connect with other people.
Verified answer
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
Hope you learnt something. Make sure to appreciate the answer if it helped you!