Need a quartic with 2 integral roots and 2 non integral roots:?

Question

Should be in general form and how to determine the roots algebraically

Answer 1

That's easy.. write it in factored form, then multiply! A quartic will have four terms, so

f(x) = (x - 1)(x - 2)(x - 1/2)(x - 1/4)

The roots are

x = 1
x = 3
x = 1/2
x = 1/4

You can substitute whatever numbers you want. I'm leaving it up to you to multiply the factors together to get the general form.

Answer 2

In general form if m and n are integers,
(x + m)(x + n) = x^2 + (m + n)x + mn
To generate a quadratic with rational, non-integer roots,
(x + m/n)(x + r/s) = x^2 + (m/n + r/s)x + (m/n)(r/s)
You can embellish by adding coefficients to one or both x's.
edit:
I read quadratic instead of quartic. To generate the desired quartic multiply the two quadratics together.