Questions: Find all real zeros of the function. [ g(x)=-4(x-9)^2(x+3)^3 ]

Find all real zeros of the function. [ g(x)=-4(x-9)^2(x+3)^3 ]
Transcript text: Find all real zeros of the function. \[ g(x)=-4(x-9)^{2}(x+3)^{3} \] If there is more than one answer, separate them with commas. zero(s): $\square$ None
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Solution

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Solution Steps

Step 1: Identify the factors of the function

The function is given as: \[ g(x) = -4(x-9)^{2}(x+3)^{3} \] The factors of the function are \((x-9)\) and \((x+3)\).

Step 2: Set each factor equal to zero

To find the zeros of the function, set each factor equal to zero: \[ (x-9) = 0 \quad \text{and} \quad (x+3) = 0 \]

Step 3: Solve for \(x\) in each equation

Solve the first equation: \[ x - 9 = 0 \implies x = 9 \] Solve the second equation: \[ x + 3 = 0 \implies x = -3 \]

The real zeros of the function are \(9\) and \(-3\).

Final Answer

\(\boxed{9, -3}\)

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