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What are the [tex]$x$[/tex]-intercepts of [tex]$f(x)=x^3+4x^2-9x-36$[/tex]?

A. [tex]$(1,0), (2,0), (3,0)$[/tex]
B. [tex]$(-4,0), (-3,0), (3,0)$[/tex]
C. [tex]$(-6,0), (2,0), (3,0)$[/tex]
D. [tex]$(-1,0), (2,0), (18,0)$[/tex]

Sagot :

GinnyAnswer
To determine the [tex]\( x \)[/tex]-intercepts of the function [tex]\( f(x) = x^3 + 4x^2 - 9x - 36 \)[/tex], we need to find the values of [tex]\( x \)[/tex] for which [tex]\( f(x) = 0 \)[/tex]. These values correspond to the roots of the equation [tex]\( x^3 + 4x^2 - 9x - 36 = 0 \)[/tex].

Given the function:
[tex]\[ f(x) = x^3 + 4x^2 - 9x - 36 \][/tex]

We need to solve the equation:
[tex]\[ x^3 + 4x^2 - 9x - 36 = 0 \][/tex]

The [tex]\( x \)[/tex]-intercepts are the points where this equation equals zero, which means finding all the real roots of the equation.

Based on our result, the roots of the equation are:
[tex]\[ x = -4, -3, 3 \][/tex]

Thus, the [tex]\( x \)[/tex]-intercepts of the equation are:
[tex]\[ (-4,0), (-3,0), (3,0) \][/tex]

Thus, the correct choice among the given options is:

B. [tex]\((-4,0), (-3,0), (3,0)\)[/tex]
wegnerkolmp2741o

Answer:

B. (-4,0), (-3,0), (3,0)

Step-by-step explanation:

f(x) = x^3 + 4x^2 -9x-36

Set the function equal to zero to find the x intercepts.

0 = x^3 + 4x^2 -9x-36

Factor by grouping.

0 = x^2(x + 4) -9(x+4)

0 = (x+4) (x^2-9)

0= (x+4)(x-3)(x+3)

Using the zero product property.

0= (x+4)   0=(x-3)   0=(x+3)

x=-4          x=3       x=-3  

(-4,0), (-3,0), (3,0)        

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