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

If y=f(x)=ax^(2)+2bx+c=0 has Imaginary roots and 4a+4b+c<0 then

If ax^(2)+bx+c=0 has imaginary roots and a,b,c in Rsuch that a+4c<2b then

If ax^(2)+bx+c = 0 has no real roots and a, b, c in R such that a + c gt 0 , then

ax^(2)+2bx-3c=0 has no real root and a+b>3(c)/(4) then

Given that ax^(2)+bx+c=0 has no real roots and a+b+c 0 d.c=0

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

If ax^(2) + bx + c = 0 has imaginary roots and a - b + c gt 0 . then the set of point (x, y) satisfying the equation |a (x^(2) + (y)/(a)) + (b + 1) x + c| = |ax^(2) + bx + c|+ |x + y| of the region in the xy- plane which is

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