Home
Class 12
MATHS
If alpha1,alpha2,alpha3,beta1,beta2,be...

If `alpha_1,alpha_2,alpha_3,beta_1,beta_2,beta_3` , are the values of n for which `sum_(r=0)^(n-1) x^(2r)` , is divisible by `sum_(r=0)^(n-1) x^r` then prove that the triangle having vertices `(alpha_1,beta_1), (alpha_2,beta_2) and (alpha_3,beta_3)` cannot be an equilateral triangle.

Promotional Banner

Similar Questions

Explore conceptually related problems

If alpha_(1), alpha_(2), alpha_(3), beta_(1), beta_(2), beta_(3) are the values of n for which sum_(r=0)^(n-1)x^(2r) is divisible by sum_(r=0)^(n-1)x^(r ) , then the triangle having vertices (alpha_(1), beta_(1)),(alpha_(2),beta_(2)) and (alpha_(3), beta_(3)) cannot be

Sum of n terms of the series sinalpha-sin(alpha+beta)+sin(alpha+2beta)-sin(alpha+3beta)+….

The lengths of the sides of a triangle are alpha-beta,alpha+beta and sqrt(3 alpha^(2)+beta^(2)),(alpha>beta>0) Its largest angle is

Find the sum of the series sinalpha+sin(alpha+beta)+sin(alpha+2beta)+sin(alpha+3beta)+.....+sin(alpha+(n-1)beta)

If alpha,beta,gamma are the real roots of the equation x^(3)-3ax^(2)+3bx-1=0 then the centroid of the triangle with vertices (alpha,(1)/(alpha))(beta,(1)/(beta)) and (gamma,1/ gamma) is at the point

Let a_(n) be the n^(th) term of an A.P.If sum_(r=1)^(100)a_(2r)=alpha&sum_(r=1)^(100)a_(2r-1)=beta, then the common difference of the A.P.is alpha-beta(b)beta-alpha(alpha-beta)/(2)quad (d) None of these

alpha , beta , gamma are the roots of the equation x^(3)-3x^(2)+6x+1=0 . Then the centroid of the triangle whose vertices are (alpha beta,1/(alpha beta)) , (beta gamma, 1/(beta gamma)) , (gamma alpha,1/(gamma alpha)) is

If alpha and beta are the roots of the equation 375x^(2)-25x-2=0, then the value of lim_(n rarr oo)(sum_(r=1)^(n)alpha^(r)+sum_(r=1)^(n)beta^(r)) is

If alpha,beta are roots of x^(2)-3x+a=0,a in R and alpha<1

if tan beta=(n sin alpha cos beta)/(1-n sin^(2)alpha) then prove that tan(alpha-beta)=(1-n)tan alpha