One of the roots of the quadratic equation is 2 times larger than the other. Find the roots and coefficient c. x ^ 2-3x + c = 0.

Suppose that the roots of this quadratic equation are equal to x1 and x2.

Then, by Vieta’s theorem, we obtain the following equalities:

x1 + x2 = 3,

x1 * x2 = s.

By the condition of the problem x1 = 2 * x2. Let’s plug this value into our equations.

2 * x2 + x2 = 3,

3 * x2 = 3,

x2 = 1.

Then x1 = 2 * x2 = 2 * 1 = 2.

Now we can find what is equal to:

1 * 2 = s,

c = 2.

Answer: x1 = 2, x2 = 1, c = 2.