One of the roots of the equation x ^ 2 + 11x + q = 0 is -7. Find the other root and the intercept q.

It is known from the condition that one of the roots of the equation x ^ 2 + 11x + q = 0; x = -7. To find what the second root is, we will use Vieta’s theorem.

Vieta’s theorem.

The roots of the complete quadratic equation ax ^ 2 + bx + c = 0 satisfy the following equalities:

x1 + x2 = -b / a;

x1 * x2 = c / a.

We write out the coefficients a and b from the given equation.

a = 1; b = 11;

Substitute Vieta’s theorem into the first equality and solve the equation:

-7 + x = -11/1;

-7 + x = -11;

x = -11 + 7;

x = -4.

We are looking for the value of q from the second equality:

-7 * (-4) = q / 1;

q = 28.

Answer: the second root of the equation is -4; q = 28.