The sum of the two roots of a quadratic is 21. The product of those two roots is 104. Given that both roots are positive, what is the difference of the two roots of the quadratic?

The difference of the two roots of the quadratic is 5

Step-by-step explanation:

Let the two roots be a and b

Sum of the roots is 21

a + b = 21 ••••••••(i)

Product of the roots is 104

ab = 104 •••••••(ii)

we want to find a - b

a = 104/b

Put this into 1

104/b + b = 21

Multiply through by b

104 + b^2 = 21b

Thus;

b^2 - 21b + 104 = 0

b^2 -13b - 8b + 104 = 0

b(b-13) -8(b -13) = 0

(b-8)(b-13) = 0

b = 8 or 13

From above;

b = 104/a

So a is 104/13 or 104/8 = 13 or 8

So the difference between the roots will just be 13-8 = 5