Question

Is it possible that the quadratic equation ax²+bx+c=0 has a positive real solution if a,b and c are all positive real numbers?

Answer 1

Not possible

Explanation:

supposing both the roots as α and β and a,b and c are all positive real numbers.

Then α+β= -b/a which will be negative

⇒ α+β<0

and αβ= c/a , which will positive

⇒αβ>0

also, -b/a>0 and c/a<0

⇒b/a<0 and c/a<0 which is not possible because all a, b and c are positive real numbers.

hence, it is not possible that the quadratic equation ax²+bx+c=0 has a positive real solution if a,b and c are all positive real numbers