Respuesta :

apologiabiology
first, simplify it, factor out any ones in the numerator and dennomenator

[tex]f(x)=\frac{2}{x^2+3x-10}[/tex]
no common factors so move to next step

set the denomenator equal to 0 because that is where the function is undefined (we can't divide by 0)

x²+3x-10=0
factor
(x-2)(x+5)=0
set to zero

x-2=0
x=2

x+5=0
x=-5


vertical assemtotes are at x=-5 and x=2

Solving a quadratic equation, it is found that the vertical asymptotes of the function are x = 2 and x = -5.

The function is given by:

[tex]f(x) = \frac{2}{x^2 + 3x - 10}[/tex]

The vertical asymptotes of a function f(x) are the values of x which are outside the function's domain.

In a fraction, the denominator cannot be zero, hence, the vertical asymptotes are found solving the following quadratic equation:

[tex]x^2 + 3x - 10 = 0[/tex]

Which has coefficients [tex]a = 1, b = 3, c = -10[/tex], and then:

[tex]\Delta = b^2 - 4ac = 3 - 4(1)(-10) = 49[/tex]

[tex]x_1 = \frac{-b + \sqrt{\Delta}}{2a} = \frac{-3 + 7}{2} = 2[/tex]

[tex]x_2 = \frac{-b - \sqrt{\Delta}}{2a} = \frac{-3 - 7}{2} = -5[/tex]

The vertical asymptotes are x = 2 and x = -5.

A similar problem is given at https://brainly.com/question/23535769

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