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Sagot :
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]
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]
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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