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murzikaleks [220]
3 years ago
7

What are the domain restrictions of the function f(x) = the quantity of x squared plus 6x plus 9, all over 3x plus 15.

Mathematics
1 answer:
dangina [55]3 years ago
6 0

Answer:

x = - 5

Step-by-step explanation:

Given

f(x) = \frac{x^2+6x+9}{3x+15}

The denominator of f(x) cannot be zero as this would make f(x) undefined. Equating the denominator to zero and solving gives the value that x cannot be.

solve : 3x + 15 = 0 ⇒ 3x = - 15 ⇒ x = - 5 ← excluded value

Domain x ∈ R , x ≠ - 5

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The roots of the given polynomials exist  $x=8+\sqrt{10}$, and $x=8-\sqrt{10}$.

<h3>What is the formula of the quadratic equation?</h3>

For a quadratic equation of the form $a x^{2}+b x+c=0$ the solutions are

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Therefore by using the formula we have

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$x_{1,2}=\frac{-(-16) \pm \sqrt{(-16)^{2}-4 \cdot 1 \cdot 54}}{2 \cdot 1}$$

simplifying the equation, we get

$&x_{1,2}=\frac{-(-16) \pm 2 \sqrt{10}}{2 \cdot 1} \\

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$x=8-\sqrt{10}$.

To learn more about quadratic equations refer to:

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