The correct option is D No real roots
Let, the age of one friend = 'x' years
Age of the other friend = '20 - x' years
Four years ago,
Age of one friend = '(x - 4)' years
Age of the other friend = '(20 - x - 4)' years
According to the condition,
(x - 4)(16 - x) = 48
⇒16x−64−x2+4x=48
⇒−x2+20x−64−48=0
⇒−x2+20x−112=0
⇒x2−20x+112=0
Here, a = 1, b = -20, c = 112
∴b2−4ac=(−20)2−4(1)(112) =400−448 =−48<0
Since b2−4ac<0, the quadratic equation has no real roots.
∴ The given situation is not possible.