If the equation `ax^2 + bx+c= 0` has non-real roots, prove that `1+c/a+b/a > 0`

If the equation ax^(2) + 2bx - 3c = 0 has non-real roots and ((3c)/(4)) lt (a + b) , then c is always :

If the equation ax^(2) + 2 bx - 3c = 0 has no real roots and (3c)/(4) lt a + b , then

If c>0 and the equation 3ax^(2)+4bx+c=0 has no real root,then

If the equation ax^(2)+bx+c=0 has two positive and real roots,then prove that the eqsition ax^(2)+(b+6a)x+(c+3b)=0 has at least one positive real root.

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

The quadratic equation ax^(2)+bx+c=0 has real roots if:

The quadratic equation ax^(2)+bx+c=0 has real roots if:

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