Question

If the arithmetic mean of the roots of the equation x(x – 2) + 4аx = 5 is 3, then a = ______.

Answer 1

If the arithmetic mean of the roots of the equation x(x – 2) + 4аx = 5 is 3, then a = –1.

Explanation:

x(x – 2) + 4ax = 5

⇒ x² + (4a – 2)x – 5 = 0

For this quadratic, the sum of the roots = –(4a – 2).

The arithmetic mean = `(-(4a - 2))/2 = 3`.

So –(4a – 2) = 6

⇒ 4a – 2 = –6

⇒ 4a = –4

⇒ a = –1