If `x_1,x_2` are the roots of `x^2-3x+a=0,a in R and x_1 < 1 < x_2` then a belongs to

Find the roots of 2x^2-3x-1=0 .

If x_(1),x_(2) are the roots of ax^(2)+bx+c=0 and x_(1)+d,x_(2)+d are the roots of px_(2)+qx+r=0, where d!=0, then

If x_(1) and x_(2) are the roots of 3x^(2)-2x-6=0 then x_(1)^(2)+x_(2)^(2) is equal to

If x_1,y_1 " are roots of " x^2+8x-20=0, x_1,y_1 " are the roots of " 4x^2+32x-57=0 and x_3,y_3 " are the roots of " 9x^2+72x-112=0 , then the points (x_1,y_1 )(x_2,y_2) and (x_3,y_3) where x_1 lt y_1 for i=1,2,3

x_1 and x_2 are the roots of a x^2+b x+c=0 and x_1x_2<0. Roots of x_1(x-x_2)^2+x_2(x-x_1)^2=0 are: (a) real and of opposite sign b. negative c. positive d. none real

x_1 and x_2 are the roots of a x^2+b x+c=0 and x_1x_2<0. Roots of x_1(x-x_2)^2+x_2(x-x_1)^2=0 are: (a) real and of opposite sign b. negative c. positive d. non real

suppose x_(1),x_(2) be the roots of ax^(2)+bx+c=0 and x_(3),x_(4) be the roots of px^(2)+qx+r=0. If x_(1),x_(2),x_(3),x_(4) are in G.P.,then its common ratio is

If x_(1),x_(2),x_(3) are the roots of x^(3)+ax^(2)+b=0, the value of x_(2)x_(3),x_(1)x_(3),x_(1),x_(2)]|

If 1,x_(1),x_(2),x_(3) are the roots of x^(4)-1=0andomega is a complex cube root of unity, find the value of ((omega^(2)-x_(1))(omega^(2)-x_(2))(omega^(2)-x_(3)))/((omega-x_(1))(omega-x_(2))(omega-x_(3)))

If 1,x_(1),x_(2),x_(3) are the roots of x^(4)-1=0andomega is a complex cube root of unity, find the value of ((omega^(2)-x_(1))(omega^(2)-x_(2))(omega^(2)-x_(3)))/((omega-x_(1))(omega-x_(2))(omega-x_(3)))