Question
If α and β are the roots of equation x2 + αx + β = 0 then find α3 + β3 = ?
Answer: Option A
$$\eqalign{
& {\text{ }}{x^2}{\text{ + }}\alpha x + \beta = 0 \cr
& {\text{Sum of root}} \cr
& \alpha + \beta = \frac{{ - \alpha }}{1}\,......(i) \cr
& \alpha \beta = \beta \,......(ii) \cr
& {\text{From (i) and (ii)}} \cr
& {\text{Then, }}\alpha = 1 \cr
& {\text{Then, }}\beta = - 2 \cr
& {\text{Then value of }} \cr
& \Leftrightarrow {\alpha ^3} + {\beta ^3} \cr
& = 1 + {\left( { - 2} \right)^3} \cr
& = - 7 \cr} $$
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$$\eqalign{
& {\text{ }}{x^2}{\text{ + }}\alpha x + \beta = 0 \cr
& {\text{Sum of root}} \cr
& \alpha + \beta = \frac{{ - \alpha }}{1}\,......(i) \cr
& \alpha \beta = \beta \,......(ii) \cr
& {\text{From (i) and (ii)}} \cr
& {\text{Then, }}\alpha = 1 \cr
& {\text{Then, }}\beta = - 2 \cr
& {\text{Then value of }} \cr
& \Leftrightarrow {\alpha ^3} + {\beta ^3} \cr
& = 1 + {\left( { - 2} \right)^3} \cr
& = - 7 \cr} $$
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