Given the roots 6 and 7, determine the quadratic equation?

To determine the quadratic equation, we'll use Viete's
relations:

x1 + x2 = S, where x1 = 6 and x2 =
7

x1 + x2 = 6+7

S =
13

x1*x2 = P

P =
6*7

P = 42

The quadratic
equation is:

x^2 - Sx + P =
0

x^2 - 13x + 42 = 0

The
quadratic equation is:

x^2 - 13x + 42 =
0

Another method of creating the quadratic when knowing the
roots is to write the equation as a product of linear
factors;

(x-x1)(x-x2) =
0

(x-6)(x-7) = 0

We'll remove
the brackets:

x^2 -6x - 7x +42 =
0

We'll combine like terms and we'll get the quadratic
equation:

x^2 - 13x + 42 =
0