x² - (Sum of the roots) x + Product of the roots = 0. Sum of the roots = 2 + i√3 + 2 - 3i ==> 4. Product of roots = (2 + i√3) (2 - i√3) = 2² - (i√3)². = 4 - 3 (-1) ==> 4 + 3 ==> 7. x² - 4 x + 7 = 0. Actually we have a polynomial of degree 4, we can split the given polynomial into two quadratic equations.
a n is called the leading coefficient of p. The rational root theorem says that if p has a rational root, then this root is equal to a fraction such that the numerator is a factor of a 0 and the denominator is a factor of a n (both positive and negative factors).
is a polynomial function with integral coefficients (a n ≠0 and a 0 ≠0) and (in lowest terms) is a rational zero of ( ), then p is a factor of the constant term a 0 and q is a factor of the leading coefficient a n . •To find the rational zeros, divide all the factors of the constant term by all the factors of the lead coefficient.