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.

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

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

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

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 (Option 1) an isosceles triangle Option 2) a right angled isosceles triangle Option 3) a right angled triangle Option 4) an equilateral triangle

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

The coordinates of the vertices of a triangle are (alpha_1 , beta_1) , (alpha_2 , beta_2) and (alpha_3 , beta_3) Prove that the coordinates of its centroid are (alpha_1 + alpha_2 + alpha_3)//(3) , (beta_1 + beta_2 + beta_3)//(3) .

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