If $α, β$ are the roots of the equation $(a x^{2} + b x + c = 0)$ , then what is the value of $α^{3} + β^{3}$ ?

\frac{b^{3} + 3 a b c}{a^{3}}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{a^{3} - b^{3}}{3 a b}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{3 a b c - b^{3}}{a^{3}}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

\frac{b^{3} - 3 a b c}{a^{3}}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C $\frac{3 a b c - b^{3}}{a^{3}}$
$α + β = - \frac{b}{a}$ and $α β = \frac{c}{a}$
$α^{3} + β^{3} = (α + β)^{3} - 3 α β (α + β)$
$= - \frac{b^{3}}{a^{3}} - 3 \frac{c}{a} \cdot (- \frac{b}{a}) = \frac{- b^{3} + 3 a b c}{a^{3}}$
$= \frac{3 a b c - b^{3}}{a^{3}}$

Suggest Corrections

Similar questions

a > b > c

a^{3} + b^{3} + c^{3} = 3 a b c,

a x^{2} + b x + c = 0

a^{3} + b^{3} + c^{3} = 3 a b c

a^{3} - b^{3} - c^{3} - 3 a b c

a^{3} + b^{3} + c^{3} - 3 a b c

The factors of $a^{3} + b^{3} + c^{3} - 3 a b c$ are

Join BYJU'S Learning Program