Hi sir, I read this statement somewhere-
For f(x)>0, Discriminant is <0
but i am unable to gather the 'why' behind it, could you please help mw with this sir?

Assuming f(x) to be a quadratic in x, then if it is greater than 0 for ALL values of x (or else less than zero for ALL values of x) what that means graphically is that it never touches the X-axis at all, i.e it never has real roots (remember that the roots are solutions for f(x) = 0, so if it never becomes zero…). Discriminant < 0 is just another way of saying no real roots. Hence these are equivalent interpretations, just that the one is graphical and the other algrebraical.

Hi sir, I read this statement somewhere-

For f(x)>0, Discriminant is <0

but i am unable to gather the 'why' behind it, could you please help mw with this sir?

Assuming f(x) to be a quadratic in x, then if it is greater than 0 for ALL values of x (or else less than zero for ALL values of x) what that means graphically is that it never touches the X-axis at all, i.e it never has real roots (remember that the roots are solutions for f(x) = 0, so if it never becomes zero…). Discriminant < 0 is just another way of saying no real roots. Hence these are equivalent interpretations, just that the one is graphical and the other algrebraical.

regards

J

okayyy sir, got it, also is there any similar interpretation for f(x)<0 as well?

Yes mentioned that also in the first line of my earlier response. Either/or.

regards

J