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=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,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 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 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

If alpha,beta be the roots of the equation x^(2)-px+q=0 then find the equation whose roots are (q)/(p-alpha) and (q)/(p-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.

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) -px + 8 = 0 , then find p, q , alpha, beta .