Which is the polynomial function of lowest degree with rational real coefficients, a leading coefficient of 3 and roots startroot 5 endroot and 2?
a) f (x) = 3 x cubed minus 6 x squared minus 15 x + 30
b) f (x) = x cubed minus 2 x squared minus 5 x + 10
c) f (x) = 3 x squared minus 21 x + 30
d) f (x) = x squared minus 7 x + 10

Step-by-step explanation:

1) In this question we've been given "a", the leading coefficient. and two roots:

2) There's a theorem, called the Irrational Theorem Root that states:

If one root is in this form  then its conjugate . is also a root of this polynomial.

Therefore

3) So, applying this Theorem we can rewrite the equation, by factoring. Remembering that x is the root. Since the question wants it in this expanded form then: