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`

Let alpha_(1),alpha_(2) and beta_(1),beta_(2) be the roots of the equation ax^(2)+bx+c=0 and px^(2)+qx+r=0 respectively.If the system of equations alpha_(1)y+alpha_(2)z=0 and beta_(1)y_(beta-)2z=0 has a non trivial solution then prove that (b^(2))/(q^(2))=(ac)/(pr)

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 and beta are the roots of the equation x^2 +x+1 = 0 , the equation whose roots are alpha^19 and beta^7 is

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

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