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, 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

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

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)

For what values of m the equation (1+m)x^(2)-2(1+3m)x+(1+8m)=0 has (m in R) (i) both roots are imaginary? (ii) both roots are equal? (iii) both roots are real and distinct? (iv) both roots are positive? (v) both roots are negative? (vi) roots are opposite in sign? (vii)roots are equal in magnitude but opposite in sign? (viii) atleast one root is positive? (iv) atleast one root is negative? (x) roots are in the ratio 2:3 ?

If a,b,c are real distinct numbers such that a ^(3) +b ^(3) +c ^(3)= 3abc, then the quadratic equation ax ^(2) +bx +c =0 has (a) Real roots (b) At least one negative root (c) Both roots are negative (d) Non real roots

Let x^2 - (m - 3) x + m = 0 (m in R) be a quadratic equation, then find the values of 'm' for which both (a) the roots are greater than 2. (b) both roots are positive, ( c) one root is positive and other is negative. ( d) One root is greater than 2 and other smaller than 1 ( e) Roots are equal in magnitude and opposite in sign, ( f) both roots lie in the interval (1, 2)

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 , 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