You visited us 1 times! Enjoying our articles? Unlock Full Access!

Common Roots

If α,β,γ ar...

Question

If $α, β, γ$ are the roots of $7 x^{3} + x - 11 = 0$ , then the equation whose roots are $- α, - β, - γ$ , is:

7 x^{3} - x + 11 = 0

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

7 x^{3} - x - 1 = 0

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

7 x^{3} + x + 11 = 0

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

7 x^{3} + x - 1 = 0

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

Open in App

Solution

The correct option is B $7 x^{3} + x + 11 = 0$
As $α, β, γ$ are roots of $7 x^{3} + x - 11 = 0$
Then to get equation whose roots are $- α, - β, - γ$ ,
Replace $x \to - x$
$7 (- x^{3}) + (- x) - 11 = 0 \Rightarrow - 7 x^{3} - x - 11 = 0 \Rightarrow 7 x^{3} + x + 11 = 0$

Suggest Corrections

Similar questions

α, β, γ

7 x^{3} - x - 2 = 0

\sum (\frac{α}{β} + \frac{β}{α})

If α, β, γ are the roots of the equation $x^{3} + 4 x + 1 = 0$ ,then $(α + β)^{- 1} + (β + γ)^{- 1} + (γ + α)^{- 1} =$

α, β, γ

x^{3} - x - 1 = 0

\frac{1}{β + γ}, \frac{1}{γ + α}, \frac{1}{α + β}

α, β, γ

x^{3} - 3 x + 11 = 0

(α + β), (β + γ)

(γ + α)

α, β, γ

a x^{3} + b x^{2} + c x + d = 0

∣ ∣ ∣ ∣ ∣ \begin{matrix} α & β & γ β & γ & α γ & α & β \end{matrix} ∣ ∣ ∣ ∣ ∣ = 0

α \neq β \neq γ

α + β - γ, γ + α - β, β + γ - α

Join BYJU'S Learning Program