Find the coefficient q of the equation x ^ 2-10x + q if one of its horses is four times larger than the other.

According to the theorem, the sum of the roots of the equation x ^ 2 + px + q = 0 is -p. In our case, p = -10, therefore the sum will be equal to:

x1 + x2 = 10 (1).

One of the roots is 4 times larger than the other, so we can write (1) as:

x1 + 4×1 = 10;

x1 = 2;

x2 = 4×1 = 4 * 2 = 8;

According to Vieta’s theorem, the coefficient q is equal to the product of roots:

q = x1 * x2 = 2 * 8 = 16.

Answer: q = 16.