If `alpha_1, alpha_2` are the roots of equation `x^2-px+1=0` and `beta_1,beta_2` be those of equation `x^2-qx+1=0` and vector `alpha_1hati+beta_1hatj` is parallel to `alpha_2hati+beta_2hatj` then (A) `p=+-q` (B) `p=+-2q` (C) `p=2q` (D) none of these

If alpha_(1),alpha_(2) are the roots of equation x^(2)-px+1=0and beta_(1),beta_(2) are those of equation x^(2)=qx+1=0 and vector alpha_(1)hat i+beta_(1)hat j is parallel to alpha_(2)hat i+beta_(2)hat j, then p=+-q b.p=+-2q c.p=2q d.none of these

If alpha_1, alpha_2 be the roots of the equation x^2-px+1=0 and beta_1,beta_2 be those of equatiion x^2-qx+1=0 and p^2=q^2,vecu=alpha_1hati+alpha_2hatj,and vecv=beta_1hati+beta_2hatj then which one is necessarily true (A) vecu_|_vecv (B) vec_|_vecw (C) vecu||vecv or vecu||vecw (D) none of these

If alpha,beta are the roots of the equation x^(2)-p(x+1)-c=0, then (alpha+1)(beta+1)=

If alpha_1, alpha_2 be the roots of equation x^2+px+q=0 and beta_1,beta be those of equation x^2+rx+s=0 and the system of equations alpha_1y+alpha_2z=0 and beta_1 y+beta_2 z=0 has non trivial solution, show that p^2/r^2=q/s

If alpha,beta are the roots of the equation x^(2)+px+q=0, then -(1)/(alpha),-(1)/(beta) are the roots of the equation.

If alpha,beta are the roots of x^(2)-px+r=0 and alpha+1,beta-1 are the roots of x^(2)-qx+r=0 ,then r is

If alpha,beta are the roots of the equation x^(2)+px+1=0 gamma,delta the roots of the equation x^(2)+qx+1=0 then (alpha-gamma)(alpha+delta)(beta-gamma)(beta+delta)=

If alpha, beta are the roots of the equations x^2+px+q=0 then one of the roots of the equation qx^2-(p^2-2q)x+q=0 is (A) 0 (B) 1 (C) alpha/beta (D) alpha beta

Let alpha,beta in R If alpha,beta^(2) are the roots of quadratic equation x^(2)-px+1=0. and alpha^(2),beta are the roots of quadratic equation x^(2)-qx+8=0, then find p,q,alpha,beta.