If `alpha_1,alpha_2` are the roots of equation `x ^2-p x+1=0a n dbeta_1,beta_2` are those of equation `x^2-q x+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=
a. +-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 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,beta are the roots of the equation x^(2)-p(x+1)-c=0, then (alpha+1)(beta+1)=

If alpha and beta are the roots of the equations x^2-p(x+1)-c=0 , then (alpha+1)(beta+1)_ is equal to:

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_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_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 the roots of the equation x^2-px+q=0 be alpha,beta and the roots of the equation x^2-ax+b=0 be alpha,1/beta then prove that, bq(a-p)^2=(q-b)^2 .

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 and beta be the roots of the equation x^2+px+q=0 show that alpha/beta is a root of the equation qx^2-(p^2-2q)x+q=0 .