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 both roots positive both roots negative one positive and one negative root both roots imaginary

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 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

The least integral value of 'a' for which the equation x^2+2(a - 1)x + (2a + 1) = 0 has both the roots positive, is

The number of integral values of a for which x^(2) - (a-1) x+3 = 0 has both roots positive and x^(2) + 3x + 6 - a = 0 has both roots negative is

If alpha and beta are the roots of the equation x^2+ax+b=0 and alpha^4 and beta^4 are the roots of the equation x^2-px+q=0 then the roots of x^2-4bx+2b^2-p=0 are always A. Can t say anything B. two positive roots C. two negative roots D. one positive and one negative root

If A, G and H are the arithmetic mean, geometric mean and harmonic mean between unequal positive integers. Then, the equation Ax^2 -|G|x- H=0 has (a) both roots are fractions (b) atleast one root which is negative fraction (c) exactly one positive root (d) atleast one root which is an integer

If alpha, beta in C are distinct roots of the equation x^2+1=0 then alpha^(101)+beta^(107) is equal to

Find the values of m for which the quadratic equation x^(2)-m(2x-8)-15=0 has (i) equal roots, (ii) both roots positive.

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