It looks like some information is missing or incomplete in your question regarding the polynomial function \( h(x) = -3x^2(5x--------+)(x- ) \). To answer it properly, I'll need clarification or correction of the polynomial, particularly the missing parts of the expression.
If we assume it's something like:
\( h(x) = -3x^2(5x + a)(x - b) \)
where \( a \) and \( b \) are constants, I can guide you through finding the zeros.
Steps to Find the Zeros of the Polynomial Function:
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Identify the Factors: The equation already has two factors, \( 5x + a \) and \( x - b \), along with the factor \( -3x^2 \).
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Set the Entire Function to Zero: To find the zeros, set \( h(x) = 0 \): \[ -3x^2(5x + a)(x - b) = 0 \]
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Find Each Factor's Zero:
- From the factor \( -3x^2 = 0 \):
- This gives \( x = 0 \) (with multiplicity 2).
- From the factor \( 5x + a = 0 \):
- Solve for \( x \): \[ 5x + a = 0 \implies x = -\frac{a}{5} \]
- From the factor \( x - b = 0 \):
- Solve for \( x \): \[ x = b \]
- From the factor \( -3x^2 = 0 \):
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List all Zeros: Based on the factors, the zeros of \( h(x) \) are:
- \( x = 0 \) (with multiplicity 2)
- \( x = -\frac{a}{5} \)
- \( x = b \)
Final Response for Question 1:
- Please provide the exact constants \( a \) and \( b \) if they are specified, or let me know the correct form of the polynomial, so I can assist you further in calculating the specific zeros.
Once you provide the additional details, I can help with graphing if that is part of your requirement. Don't forget to sketch the polynomial and label the zeros!
3 answers