To find a polynomial of degree 3 with real coefficients given three roots, you can follow these steps:
Step 1: Identify the roots.
The roots given to us are 1, -2, and 3.
Step 2: Write down a polynomial factored form.
A polynomial of degree 3 with three roots can be written as f(x) = (x - r1)(x - r2)(x - r3), where r1, r2, r3 are the roots of the polynomial.
Step 3: Substitute the roots into the polynomial.
Substituting our identified roots into the polynomial gives us:
f(x) = (x - 1)(x - (-2))(x - 3)
This simplifies to:
f(x) = (x - 1)(x + 2)(x - 3)
So the polynomial of degree three with real coefficients, that has the roots 1, -2, and 3, is f(x) = (x - 1)(x + 2)(x - 3). This polynomial is the required solution.