Home
Class 12
MATHS
Let alpha and beta be the roots of x^2-6...

Let `alpha` and `beta` be the roots of `x^2-6x-2=0` with `alpha>beta` if `a_n=alpha^n-beta^n` for ` n>=1` then the value of `(a_10 - 2a_8)/(2a_9)`

A

1

B

2

C

3

D

4

Text Solution

Verified by Experts

The correct Answer is:
C
` a_(n) = a^(n) - beta^(n)`
Also `alpha^(8)` on both sides
`rArr alpha ^(10) - 6alpha ^(9) - 2 alpha^(8) = 0` (1)
Similarly ` beta ^(10) - 6 beta^(9) - 2 beta ^(8) = 0 ` (2)
Subtracting (2) from (1) we have
` alpha ^(10) - beta^(10) - 6 (alpha ^(9) - beta^(9)) = 2 (alpha ^(8) - beta^(8))`
`rArr a_(10) - 6 a_(9) = 2a_(8)`
`rArr (a_(10) - 2 a_(8))/(2a_(9)) = 3 `
Promotional Banner

Topper's Solved these Questions

  • THEORY OF EQUATIONS

    CENGAGE PUBLICATION|Exercise JEE ADVANCED (Multiple Correct Answer Type )|1 Videos

  • THEORY OF EQUATIONS

    CENGAGE PUBLICATION|Exercise JEE ADVANCED (Multiple Correct Answer Type )|2 Videos

  • THEORY OF EQUATIONS

    CENGAGE PUBLICATION|Exercise Archives JEE MAIN (single correct Answer Type )|7 Videos

  • STRAIGHT LINES

    CENGAGE PUBLICATION|Exercise ARCHIVES (NUMERICAL VALUE TYPE)|1 Videos

  • THREE DIMENSIONAL GEOMETRY

    CENGAGE PUBLICATION|Exercise All Questions|291 Videos

Similar Questions

Explore conceptually related problems

Let alpha and beta be the roots of the equation x^2-6x-2=0 . If a_n=alpha^n-beta^n , for nge1 , then the value of (a_10-2a_8)/(2a_9) is equal to

Let alpha, beta be the roots of the equation x^(2)-6x-2=0 with alpha gt beta . If a_(n)=alpha^(n)-beta^(n) for n ge 1 , then the value of (a_(10)-2a_(8))/(2a_(9)) is

Let alpha and beta be the roots of equation x^(2)-6x-2=0." If " a_(n)=alpha^(n)-beta^(n)," for "nge1 , "then the value of " ((a_(10))-(2a_(8)))/(2a_(9)) is equal to -

IF alpha and beta be the roots of the equation ax^2+bx+c=0 , find the values of alpha^2+beta^2

Let alphaandbeta be the roots of x^(2)+x+1=0 . If n be positive integer, then alpha^(n)+beta^(n) is

IF alpha and beta are the roots of the equation x(x-3)=4, find the value of alpha^2+beta^2 .

If alpha and beta are the roots of x^2-x+1=0 ,then the value of alpha^(2013)+beta^(2013) is equal to

Let alpha,beta be the roots of x^2-x-1=0 and S_n=alpha^n+beta^n , for all integers nge1 . Then for every integer nge2 ,

Let alpha,beta be the roots of x^(2)-x-1=0ands_(n)=alpha^(n)+beta^(n) for all integers nge1 . Then for every integer nge2 -

If alpha, beta are the roots of x^(2) - px + q = 0 and alpha', beta' are the roots of x^(2) - p' x + q' = 0 , then the value of (alpha - alpha')^(2) + (beta -alpha')^(2) + (alpha - beta')^(2) + (beta - beta')^(2) is