Find the quadratic equation whose roots are at x = 3 and x = 5.

We need to determine the quadratic equation whose roots
are 3 and 5.

There are two ways to find the
equation.

We will use the factors method to determine  the
function.

We find the factors of the quadratic
function.

Let f(x) be the function where 3 and 5 are the
roots.

==> Then, the factors are (x-3) and
(x-5)

==> f(x) =
(x-3)(x-5)

We will open the
brackets.

==> f(x) = x^2 -3x -5x +
15

==> f(x) = x^2 - 8x +
15