MyQuestionIcon

1

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

Relation between Roots and Coefficients for Higher Order Equations

If α , β , γ ...

Question

If $α, β, γ$ are the roots of $x^{3} + 3 x^{2} + 4 x + 5 = 0$ , then which of the following is/ are true.

A

\sum β^{2} γ^{2} = - 14

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

B

\sum \frac{1}{α} = - \frac{4}{5}

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

C

\sum α^{2} = 1

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

D

\sum α = 3

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

Open in App

Solution

The correct option is C $\sum α^{2} = 1$
$α + β + γ = - 3 α β + β γ + γ α = 4, α β γ = - 5$

$\sum \frac{1}{α} = \frac{α β + β γ + γ α}{α β γ} = - \frac{4}{5}$

$\sum α^{2} = (α + β + γ)^{2} - 2 (α β + β γ + γ α) = 9 - 8 = 1$

$\sum β^{2} γ^{2} = (α β + β γ + γ α)^{2} - 2 α β γ (α + β + γ) = 16 - 2 (- 5) (- 3) = - 14$

Suggest Corrections

thumbs-up

0

Similar questions

α, β, γ

are the roots of

x^{3} + 3 x^{2} + 4 x + 5 = 0

, then which of the following is/ are true.

α

β

γ

are the roots of

x^{3} + 3 x^{2} - 4 x + 2 = 0

then the equation whose roots are

\frac{1}{α β}

\frac{1}{β γ}

\frac{1}{γ α}

α, β, γ

are the roots of

x^{3} - 3 x^{2} + 4 x - 7 = 0

(α + 2) (β + 2) (γ + 2) =

α, β, γ

are the roots of the equation

x^{3} + 4 x + 1 = 0

(α + β)^{- 1} + (β + γ)^{- 1} + (γ + α)^{- 1} =

α, β

γ

are roots of the cubic equation

x^{3} + 3 x^{2} + 3 x + 2 = 0

, then the value of

(α + β + γ)

View More

Join BYJU'S Learning Program

explore_more_icon

Explore more

Relation between Roots and Coefficients for Higher Order Equations

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon