One of the roots of this quadratic equation is -3. Find the coefficient k and the second root

One of the roots of this quadratic equation is -3. Find the coefficient k and the second root of the equation x ^ 2 + kx + 18 = 0.

It is known from the condition that one of the roots of the equation x ^ 2 + kx + 18 = 0; x = -3. To find what is the second root and the coefficient k, we will use Vieta’s theorem.

Vieta’s theorem.

The roots of the complete quadratic equation ax2 + bx + c = 0 satisfy the following equalities:

x1 + x2 = -b / a;

x1 * x2 = c / a.

Let’s write out the coefficients a and c from the given equation.

a = 1; c = 18;

Substitute Vieta’s theorem into the second equality and get the equation:

-3x = 18/1;

-3x = 18;

x = 18: (-3);

x = -6.

Now let’s find the second coefficient:

x1 + x2 = -k / a;

-3 – 6 = -k / 1;

-9 = -k;

k = 9.

Answer: the second root of the equation is -6; k = 9.