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?

Not possible

Step-by-step 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

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