The roots of the equation `ax^2+bx + c = 0` will be imaginary if, A)`a gt 0 b=0 c lt 0` B) `a gt 0 b =0 c gt 0` (C) `a=0 b gt 0 c gt 0` (D) `a gt 0, b gt 0 c =0`

State the roots of quadratic equation ax^(2)+bx+c=0" if "b^(2)-4ac gt0

If a lt 0 and b lt 0 , then (a +b)^(2) gt 0 .

Let alpha and beta (a lt beta) " be the roots of the equation " x^(2) + bx + c = 0," where " b gt 0 and c lt 0 . Consider the following : 1. alpha + beta + alpha beta gt 0 2. alpha^(2) beta + beta ^(2) alpha gt 0 Which of the above is//are correct ?

Let a gt 0, b gt 0 then both roots of the equation ax^(2)+bx+c=0

In a quadratic equation ax^(2) + bx + c = 0 "if" b^(2) - 4ac gt 0 then their roots are ….

If a, c gt 0 and ax^2 + 2bx + 3c = 0 does not have any real roots then prove that: (i) 4a-4b + 3c gt 0 , (ii) a + 6b + 27c gt 0 , (iii) a + 2b + 6c gt 0

The least value of the function f(x)=ax+(b)/(x) is …………… (Where a gt 0, b gt 0, c gt 0 )

The least value of the function f(x) = ax + (b)/(x) (x gt 0, a gt 0, b gt 0)