Question

Which is the polynomial function of lowest degree with rational real coefficients, a leading coefficient of 3 and roots

Answer 1

Answer:

f(x) = $3x^{3} - 6x^{2} - 15x + 30$

Step-by-step explanation:

If  $\sqrt{5}$  is a root, then so is -$\sqrt{5}$

f(x) = 3(x + $\sqrt{5}$)(x - $\sqrt{5}$)(x - 2)

     = $3(x^{2} - 5)(x - 2)$

     = 3($x^{3} - 2x^{2} - 5x + 10$)

     = $3x^{3} - 6x^{2} - 15x + 30$