If - - Y are the roots of x 3- x 2-1-0- then the value of 1-1-1-1-1- Y -1- Y -A- -7B- -5C- -6D- -2

The correct option is B 5 x^3 x^2 1 = 0 α + β + γ = 1, αβ + βγ + γα = 0, αβγ = 1. Now, 1 + α/1 α = 2 (1 α)/1 α = 2/1 α 1 ∴∑1 + α/1 α = ∑2/1 ...

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

Byju's Answer

Standard XII

Mathematics

Relation between Roots and Coefficients for Quadratic

If α, β, Y ar...

Question

If $α, β, γ$ are the roots of $x^{3} - x^{2} - 1 = 0,$ then the value of $\frac{1 + α}{1 - α} + \frac{1 + β}{1 - β} + \frac{1 + γ}{1 - γ} =$

- 5

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

- 6

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

- 7

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

- 2

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

Open in App

Solution

The correct option is A
- 5

$x^{3} - x^{2} - 1 = 0 α + β + γ = 1, α β + β γ + γ α = 0, α β γ = 1.$
Now, $\frac{1 + α}{1 - α} = \frac{2 - (1 - α)}{1 - α} = \frac{2}{1 - α} - 1 ∴ \sum \frac{1 + α}{1 - α} = \sum \frac{2}{1 - α} - \sum 1 = 2 \sum \frac{1}{1 - α} - 3 (i) N o w, \frac{1}{x - α} + \frac{1}{x - β} + \frac{1}{x - γ} = \frac{(x - β) (x - γ) + (x - α) (x - β) + (x - α) (x - γ)}{(x - α) (x - β) (x - γ)} \frac{1}{x - α} + \frac{1}{x - β} + \frac{1}{x - γ} = \frac{3 x^{2} - 2 x}{x^{3} - x^{2} - 1} L e t x = 1 = \frac{1}{1 - α} + \frac{1}{1 - β} + \frac{1}{1 - γ} = \frac{3 - 2}{1 - 1 - 1} = - 1 ∴ (i) = 2 (- 1) - 3 = - 5$

Suggest Corrections

Similar questions

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

If $α, β, γ$ are the roots of $x^{3} - x^{2} - 1$ = 0, then the value of $\frac{1 + α}{1 - α} + \frac{1 + β}{1 - β} + \frac{1 + γ}{1 - γ}$ is equal to:

Q. If

α, β, γ

are roots of equation

x^{3} - x - 1 = 0

, then the equation whose roots are

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

is -

Q. If

α, β, γ

are roots of

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

the value of

\frac{1 + α}{1 - α} + \frac{1 + β}{1 - β} + \frac{1 + γ}{1 - γ} =

$α$ , $β$ , $γ$ are the roots of $x^{3} - 3 x^{2}$ + 3x + 7 = 0(w is cube root of unity) then $(\frac{α - 1}{β - 1} + \frac{β - 1}{γ - 1} + \frac{γ - 1}{α - 1})$ is

Join BYJU'S Learning Program

If α,β,γ are the roots of x3−x2−1=0, then the value of 1+α1−α+1+β1−β+1+γ1−γ=

If $α, β, γ$ are the roots of $x^{3} - x^{2} - 1 = 0,$ then the value of $\frac{1 + α}{1 - α} + \frac{1 + β}{1 - β} + \frac{1 + γ}{1 - γ} =$