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

If a , b , c are positive numbers such that a gt b gt c and the equation (a+b-2c)x^(2)+(b+c-2a)x+(c+a-2b)=0 has a root in the interval (-1,0) , then

If a, b, c are distinct positive rational numbers and they are in A.P., then the roots of the equation ax^(2) +2bx+x=0 are-

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 a ,b , and c are in A.P. and one root of the equation a x^2+bx+c=0 is 2, the find the other root dot

If b gt 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)

Both the roots of the equation (x-b)(x-c)+(x-a)(x-c)+(x-a)(x-b)=0 are always a. positive b. real c. negative d. none of these

If alphaa n dbeta are the roots of x^2+p x+q=0a n dalpha^4,beta^4 are the roots of x^2-r x+s=0 , then the equation x^2-4q x+2q^2-r=0 has always. A. one positive and one negative root B . two positive roots C . two negative roots D . cannot say anything

If the equation a x^2+b x+c=0 has two positive and real roots, then prove that the equation a x^2+(b+6a)x+(c+3b)=0 has at least one positive real root.

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