Question

Which is the polynomial function of lowest degree with rational real coefficients, a leading coefficient of 3 and roots StartRoot 5 EndRoot and 2?

Answer 1

Answer:

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

Or

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

Step-by-step explanation:

For a polynomial function of lowest degree with rational real coefficients, each root has multiplicity of 1.

The polynomial has roots $x=\sqrt{5}$ and 2 with a leading coefficient of 3.

By the irrational root theorem of polynomials, $x=-\sqrt{5}$ is also a root of the required polynomial.

By the factor theorem, we can write the polynomial in factored form as:

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

We expand, applying difference of two squares to obtain

$f(x)=3(x-2)(x^2-5)$

We expand further using the distributive property to get:

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

Answer 2

Answer:

A on edgegentuyuyuyuy

Step-by-step explanation: