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Ratling [72]
2 years ago
12

F(x)= (x-1)(x(x+1)+2x) find all rational zeros​

Mathematics
1 answer:
pantera1 [17]2 years ago
5 0

Answer:

x = 0, x = 1, x = - 3

Step-by-step explanation:

To find the zeros, let f(x) = 0 , that is

(x - 1)(x(x + 1) + 2x) = 0  ← distribute and simplify parenthesis

(x - 1)(x² + x + 2x) = 0

(x - 1)(x² + 3x) = 0 ← factor out x from the second parenthesis

x(x - 1)(x + 3) = 0

Equate each factor to zero and solve for x

x = 0

x - 1 = 0 ⇒ x = 1

x + 3 = 0 ⇒ x = - 3

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Rudiy27

Answer:   \bold{D.\ \dfrac{x+4}{x}\ where\ x \neq 0, \dfrac{2}{3}}

<u>Step-by-step explanation:</u>

f(x) = 3x² + 10x - 8

g(x) = 3x² - 2x


\dfrac{f(x)}{g(x)}=\dfrac{3x^2+10x-8}{3x^2-2x}=\dfrac{(3x-2)(x+4)}{x(3x-2)}=\dfrac{x+4}{x}

Restriction on x: the denominator cannot be equal to zero. So,

    x(3x - 2) ≠ 0  

→  x ≠ 0     and     3x - 2 ≠ 0

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