If 1 is a 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 c lt a lt b lt d , then roots of the equation bx^(2)+(1-b(c+d)x+bcd-a=0

If b^2<2a c , then prove that a x^3+b x^2+c x+d=0 has exactly one real root.

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 in R^+a n d2b=a+c , then check the nature of roots of equation a x^2+2b x+c=0.

Prove that the roots of the equation (a^4+b^4)x^2+4a b c dx+(c^4+d^4)=0 cannot be different, if real.

If a

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)

If c ,d are the roots of the equation (x-a)(x-b)-k=0 , prove that a, b are roots of the equation (x-c)(x-d)+k=0.

If the equation whose roots are the squares of the roots of the cubic x^3-a x^2+b x-1=0 is identical with the given cubic equation, then (a) a=0,b=3 b. a=b=0 c. a=b=3 d. a ,b , are roots of x^2+x+2=0

The number of roots of the equation xsinx=1,x in [-2pi,0)uu(0,2pi] is 2 (b) 3 (c) 4 (d) 0