Home
Class 12
MATHS
If alpha, beta are the roots of the equ...

If ` alpha, beta` are the roots of the equation ` x^(2) - 2x + 4 = 0 ` then for any`n in N` show that ` alpha^(n) + beta^(n) = 2^(n+1) cos ((n pi)/3)`.

Text Solution

Verified by Experts

The correct Answer is:
`2^(n+1)cos""(pi)/(3)`
Promotional Banner

Topper's Solved these Questions

  • MODEL PAPER 5

    VGS PUBLICATION-BRILLIANT|Exercise Sectio - B (Short Answer type questions)|10 Videos

  • MATHEMATICS-II(B) MODEL PAPER 4

    VGS PUBLICATION-BRILLIANT|Exercise Section-C|7 Videos

  • MODEL PAPER 6

    VGS PUBLICATION-BRILLIANT|Exercise Section -C (Long Answer Type Questions)|7 Videos

Similar Questions

Explore conceptually related problems

If alpha,beta are the roots of the equation x^(2) - 4x + 8 = 0 . Them for any ninN,alpha^(2n)+beta^(2n) equals

If alpha,beta are roots of the equation x^(2)-4x+8=0 then for any ninN,alpha^(2n)+beta^(2n)

If alpha and beta are the roots of the equation x^2-2x+4=0, then alpha ^9 + beta ^9=

If alpha, beta are the roots of the equation x^(2) + x + 1 = 0 then prove that alpha^(4) + beta^(4) + alpha^(-1) beta^(-1) = 0 .

If alpha , beta , gamma are the roots of the equation x^3 +4x^2 -5x +3=0 then sum (1)/( alpha^2 beta^2)=

"If" alpha and beta are the roots of the quadratic equation 2x^(2) + 3x - 7 = 0 "then" (alpha^(2) + beta^(2))/(alpha beta)=