If `a+ b+ c gt ( 9c)/( 4) `and the equation `ax^(2) + 2bx -5c =0` has non-real complex roots, then

If a + b + c >(9c)/4 and quadratic equation ax^2 + 2bx-5c = 0 has non-real roots, then-

If the equation ax^(2) + bx + c = 0, a,b, c, in R have non -real roots, then

If a + b + c = 0 then the quadratic equation 3ax^(2) + 2bx + c = 0 has

If a, b, c ∈ R, a ≠ 0 and the quadratic equation ax^2 + bx + c = 0 has no real root, then show that (a + b + c) c > 0

a, b, c, in R, a ne 0 and the quadratic equation ax^(2) + bx + c = 0 has no real roots, then which one of the following is not true?

If the equation ax^2 + bx + c = 0, 0 < a < b < c, has non real complex roots z_1 and z_2 then

Given a,b, c are three distinct real numbers satisfying the inequality a-2b+4c gt0 and the equation ax ^(2) + bx +c =0 has no real roots. Then the possible value (s) of (4a +2b+c)/(a+3b+9c) is/are:

If the equation cx^(2)+bx-2a=0 has no real roots and a lt (b+c)/(2) then

If the equation cx^(2)+bx-2a=0 has no real roots and a lt (b+c)/(2) then

If 0 lt a lt b lt c and the roots alpha,beta of the equation ax^2 + bx + c = 0 are non-real complex numbers, then