If `b > a ,` then the equation `(x-a)(x-b)-1=0` has (a) both roots in `(a ,b)` (b) both roots in `(-oo,a)` (c) both roots in `(b ,+oo)` (d)one root in `(-oo,a)` and the other in `(b ,+oo)`

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 a ,b ,c in Ra n da b c<0 , then equation b c x^2+2(b+c-a)x+a=0h a s (a)both positive roots (b)both negative roots (c)real roots (d)one positive and one negative root

The quadratic equation (x-a)(x-b)+(x-b)(x-c)+(x-c)(x-a)=0 has equal roots if

If alpha, beta are the roots of the equation (x-a)(x-b)=5 then the roots of the equation (x- alpha)(x-beta)+5=0 are

The equation x-2/(x-1)=1-2/(x-1) has a. no root b. one root c. two equals roots d. Infinitely many roots

If a,b,c in R and a+b+c=0, then the quadratic equation 3ax^2+2bx+c=0 has (a) at least one root in [0, 1] (b) at least one root in [1,2] (c) at least one root in [3/2, 2] (d) none of these

If 3(a+2c)=4(b+3d), then the equation a x^3+b x^2+c x+d=0 will have (a)no real solution (b)at least one real root in (-1,0) (c)at least one real root in (0,1) (d)none of these

If positive numbers a ,b ,c are in H.P., then equation x^2-k x+2b^(101)-a^(101)-c^(101)=0(k in R) has (a)both roots positive (b)both roots negative (c)one positive and one negative root (d)both roots imaginary

If a ,b ,c ,d in R , then the equation (x^2+a x-3b)(x^2-c x+b)(x^2-dx+2b)=0 has a. 6 real roots b. at least 2 real roots c. 4 real roots d. none of these

If the quadratic equation 4x^2-2(a+c-1)x+a c-b=0(a > b > c) (a)Both roots se greater than a (b)Both roots are less than c (c)Both roots lie between c/2 and a/2 (d)Exactly one of the roots lies between c/2 and a/2