Question

$\alpha {}^{3} + \beta {}^{3}$
If alpha and beta are roots of equation = ax2 + bx + c = 0 . find the value of alpha cube + beta cube ​

Answer 1

Given Question :-

α³ +β³

If alpha and beta are roots of equation = ax2 + bx + c = 0 . find the value of alpha cube + beta cube

Answer:-

Given :-

• Alpha and Beta are roots of equation = ax2 + bx + c = 0

Find :-

• value of alpha cube + beta cube (α³ + β³)

Solution :-

α and β are the zeroes of given polynomial . Hence ,

$: \Longrightarrow \sf{\alpha+\beta = - \dfrac{b}{a} }$

$: \Longrightarrow \sf{\alpha\beta = \dfrac{c}{a} }$

Therefore ,

$: \Longrightarrow\sf{ \alpha ^ 3+ \beta^3=( \alpha+ \beta)^3-3\alpha\beta(\alpha+ \beta)}$

$: \Longrightarrow\sf{\alpha^3+\beta^3=(\dfrac{-b}{a})^3 - \dfrac{3c}{a}( - \dfrac{b}{a})}$

$: \Longrightarrow\sf{\alpha^3+\beta^3=\dfrac{-b^3}{a^3} + \dfrac{3bc}{a^2}}$

$: \Longrightarrow \sf{\alpha^3+\beta^3=\dfrac{-b^3+3abc}{a^3}}$