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

Relations between Roots and Coefficients : Higher Order Equations

If α, β and γ...

Question

If $α, β$ and $γ$ are the roots of $x^{3} + 8 = 0$ , then the equation whose roots are $α^{2}, β^{2} a n d γ^{2}$ is

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

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

Open in App

Solution

The correct option is D

Let $y = x^{2}$ . then $x = \sqrt{y}$

∴ $x^{3} + 8 = 0$ ⇒ $y^{\frac{3}{2}} + 8 = 0$

⇒ $y^{3} = 64$ ⇒ $y^{3} - 64 = 0$

Thus the equation having roots $α^{2}, β^{2}$ and $γ^{2} i s x^{3} - 64 = 0$

Suggest Corrections

Similar questions

α, β, γ

x^{3} - 7 x + 6 = 0

{(α + β)}^{2}, {(β + γ)}^{2}, {(γ + α)}^{2}

α, β, γ

x^{3} + q x + r = 0

{(α - β)}^{2}, {(β - γ)}^{2}, {(γ - α)}^{2}

α, β, γ

x^{3} - 7 x + 6 = 0

(α - β)^{2}, (β - γ)^{2}, (γ - α)^{2}

α, β, γ

x^{3} - 6 x^{2} + 11 x - 6 = 0

α^{2} + β^{2}, β^{2} + γ^{2}, γ^{2} + α^{2}

α + β + γ = 2, α^{2} + β^{2} + γ^{2} = 6

α^{3} + β^{3} + γ^{3} = 8

α, β, γ

Join BYJU'S Learning Program