If `A=[[a,b],[c,d]]` (where `b c!=0` ) satisfies the equations `x^2+k=0,t h e n`

The number of ordered pairs which satisfy the equation x^2+2xsin(x y)+1=0 are (where y in [0,2pi] ) (a) 1 (b) 2 (c) 3 (d) 0

Suppose A, B, C are defined as A=a^2b+a b^2-a^2c-a c^2 , B=b^2c+b c^2-a^2b-a b^2 - bc^2, and C=a^2c +'a c^2-b^2' c-b c^2, w h e r ea > b > c >0 and the equation A x^2+B x+C=0 has equal roots, then a ,b ,c are in AdotPdot b. GdotPdot c. HdotPdot d. AdotGdotPdot

If z_1a n dz_2 are the complex roots of the equation (x-3)^3+1=0,t h e nz_1+z_2 equal to a. 1 b. 3 c. 5 d. 7

If a,b,c are in G.P., then the equations ax^2+2bx+c =0 and dx^2+2ex+f =0 have a common root if d/a,e/b,f/c are in

If 1 is the twice repeated root of the equation a x^3+b x^2+b x+d=0,t h e n (a) a=b=d (b) a+b=0 (c) b+d=0 (d) a=d

If f(x)=a+b x+c x^2 and alpha,beta,gamma are the roots of the equation x^3=1,t h e n \ |[a,b,c],[b,c,a],[c,a,b]| is equal to

If the sines of the angles A and B of a triangle ABC satisfy the equation c^2x^2-c(a+b)x+a b=0 , then the triangle (a) is acute angled (b) is right angled (c) is obtuse angled (d) satisfies the equation sinA+cosA ((a+b))/c

If the roots of the equation x^3+P x^2+Q x-19=0 are each one more that the roots of the equation x^3-A x^2+B x-C=0,w h e r eA ,B ,C ,P ,a n dQ are constants, then find the value of A+B+Cdot

If sinthetaa n d-costheta are the roots of the equation a x^2-b x-c=0 , where a , ba n dc are the sides of a triangle ABC, then cosB is equal to 1-c/(2a) (b) 1-c/a 1+c/(c a) (d) 1+c/(3a)

Let a ,b , c in R such that no two of them are equal and satisfy |(2a, b, c),( b, c,2a), (c, 2a, b)|=0, then equation 24 a x^2+8b x+4c=0 has (a) at least one root in [0,1] (b) at least one root in [-1/2,1/2] (c) at least one root in [-1,0] (d) at least two roots in [0,2]