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 roots of the equation (b-c) x^2 +(c-a)x+(a-b)=0 are

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

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.

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 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 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 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 a, b, c in R and the quadratic equation x^2 + (a + b) x + c = 0 has no real roots then