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?
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

Answer 1

Answer:

its a

Step-by-step explanation:

Answer 2

Answer:

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

Step-by-step explanation:

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

$x_{1}=\sqrt{5}\:x_{2}=2$

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

If one root is in this form $x'=\sqrt{a}+b$  then its conjugate $x''=\sqrt{a}-b$. is also a root of this polynomial.

Therefore

$x_3=-\sqrt{5}$

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:

$f(x)=3(x-\sqrt{5})(x+\sqrt{5})(x-2)\Rightarrow 3x^{3}-6x^{2}-15x+30$