The quadratic equation for roots x1 and x2 and leading coefficient a can be written as:

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

In our case x1 = 1, x2 = 3, and a = 3, that is:

3(x - 1)(x - 3) = 0

3(x^2 - 3x - x + 3) = 0

3(x^2 - 4x + 3) = 0

3x^2 - 12x + 9 = 0

........

click here to see the solution of the quadratic equation

Indeed, the roots are 1 and 3.

The quadratic equation whose roots are 1 and 3, and whose leading coefficient is 3 is 3x^2 - 12x + 9 = 0.