The equation x ^ 2 + px + q = 0 has roots -4 and 3. Find p

If x1 and x2 are the roots of the quadratic equation x ^ 2 + px + q = 0, then by Vieta’s theorem we can write:

x1 + x2 = -p;

x1 * x2 = q.

Since, by condition, the roots of the given equation are x1 = -4, x2 = 3, then:

-4 + 3 = -p;

-4 * 3 = q;

-1 = -p; 1 = p;

-12 = q.

Then the original equation can be written as:

x ^ 2 + 1 – 12 = 0.

Answer: p = 1, q = -12.