if `ax^2+bx+c = 0` has imaginary roots and `a+c lt b` then prove that `4a+c lt 2b`

ax^2 + bx + c = 0(a > 0), has two roots alpha and beta such alpha 2, then

If ax^2 + bx + c = 0, a, b, c in R has no real zeros, and if a + b + c + lt 0, then

If ax^(2) + bx + c = 0 , a , b, c in R has no real roots, and if c lt 0, the which of the following is ture ? (a) a lt 0 (b) a + b + c gt 0 (c) a +b +c lt 0

If the equation x^2 + bx + ca = 0 and x^2 + cx + ab = 0 have a common root and b ne c , then prove that their roots will satisfy the equation x^2 + ax + bc = 0 .

If ax^(2)+ bx +c and bx ^(2) + ax + c have a common factor x +1 then show that c=0 and a =b.

If the equation ax^2 + bx + c = 0 ( a gt 0) has two roots alpha and beta such that alpha 2 , then

Consider a quadratic equation ax^2 + bx + c = 0 having roots alpha, beta . If 4a + 2b + c > 0,a-b+c 0 then |[alpha] + [beta]| can be {where [] is greatest integer}

If the sum of the roots of the quadratic equation ax^(2) + bx + c = 0 is equal to the sum of the squares of their reciprocals, then prove that 2a^(2)c = c^(2)b + B^(2)a.

If the equation ax^(2)+bx+c=0, a gt 0 , has two distinct real roots alpha" and "beta such that alpha lt -5" and "beta gt 5 , then

If a,b,c are real numbers such that 0 lt a lt 1, 0 lt b lt 1, 0 lt c lt 1, a + b + c = 2 , then prove that (a)/(1 - a) (b)/(1 - b) (c )/(1 - c) ge 8 .