If α, β, γ and δ are the roots of $x^{4} + 2 x^{3} + 3 x^{2} + 4 x + 5 = 0$ .
Find the equation whose roots are $\frac{1}{α}, \frac{1}{β}, \frac{1}{γ}, \frac{1}{δ}$ .

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

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

5 $x^{4} + 4 x^{3} + 3 x^{2} + 2 x + 1 = 0$

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

5 $x^{4} - 4 x^{3} + 3 x^{2} - 2 x + 1 = 0$

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

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

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

Open in App

Solution

The correct option is B
5 $x^{4} + 4 x^{3} + 3 x^{2} + 2 x + 1 = 0$

Given: $x^{4} + 2 x^{3} + 2 x^{2} + 4 x + 5 = 0 . . . (1)$ have roots as α, β, γ, δ.

Changing $x$ to $\frac{1}{x}$

$\Rightarrow \frac{1}{x^{4}} + \frac{2}{x^{3}} + \frac{3}{x^{2}} + \frac{4}{x} + 5 = 0$

$\Rightarrow 5 x^{4} + 4 x^{3} + 3 x^{2} + 2 x + 1 = 0 . . . (2)$

Roots of the equation (2) being the reciprocal of the roots of the equation (1) i.e., $\frac{1}{α}$ , $\frac{1}{β}$ , $\frac{1}{γ}$ , $\frac{1}{δ}$ .
Hence the required equation is
$\Rightarrow 5 x^{4} + 4 x^{3} + 3 x^{2} + 2 x + 1 = 0$

Suggest Corrections

Similar questions

If α, β, γ and δ are the roots of $x^{4} + 2 x^{3} + 3 x^{2} + 4 x + 5 = 0$ .
Find the equation whose roots are $\frac{1}{α}, \frac{1}{β}, \frac{1}{γ}, \frac{1}{δ}$ .

Q. If

α, β, γ, δ

are the roots of the equation

x^{4} - 2 x^{3} + 2 x^{2} + 1 = 0

, then the equation whose roots are

2 + \frac{1}{α}, 2 + \frac{1}{β}, 2 + \frac{1}{γ}, 2 + \frac{1}{δ}

, is:

Q. If

α, β, γ, δ

are the roots of the equation

x^{4} + q x^{2} + r x + s = 0

find the equation whose roots are

β + γ + δ + (β γ δ)^{- 1}

, and

c

Q. If

α

and

β

are roots of

x^{2} + p x + 1 = 0

, and

γ

and

δ

are the roots of

x^{2} + q x + 1 = 0

show that

q^{2} - p^{2} - (α - γ) (β - γ) (α + δ) (β + δ) = 0

If ∝ and β are roots of $x^{2}$ + ax - b = 0 and γ, δ arethe roots of $x^{2}$ + ax + b = 0, then (α-γ) (β-δ) (α-δ) (β-γ)

Join BYJU'S Learning Program

If α, β, γ and δ are the roots of x4+2x3+3x2+4x+5=0. Find the equation whose roots are 1α,1β,1γ,1δ.

If α, β, γ and δ are the roots of $x^{4} + 2 x^{3} + 3 x^{2} + 4 x + 5 = 0$ .
Find the equation whose roots are $\frac{1}{α}, \frac{1}{β}, \frac{1}{γ}, \frac{1}{δ}$ .