Question

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?

Answer 1

The difference of the two roots of the quadratic is 5

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