We have a quadratic equation $ax^2$+ $bx$ + c =0 . It has no real roots. i.e $b^2$- $4ac$ < 0 .What is the sign of c ?
My tries- I have supposed the $4ac$ will be greater than $b^2$ , because if it wasn’t then the roots will never be less then zero . So Two cases arise-
1- Both $a$ and $c$ are greater then zero.
2- Both $a$ and $c$ are smaller then zero.
So $c$ could be greater than zero or smaller than zero .
But my book says, $c<0$ . WHY?