If the product of the roots of
`4x^3+16x^2-9x-a=0` is 9 , then find a .

Answer

To solve the problem, we need to find the value of \( a \) given that the product of the roots of the polynomial \( 4x^3 + 16x^2 - 9x - a = 0 \) is equal to 9.

### Step 1: Identify the coefficients
The given polynomial is:
\[ 4x^3 + 16x^2 - 9x - a = 0 \]
We can compare this with the general form of a cubic equation:
\[ ax^3 + bx^2 + cx + d = 0 \]
From this comparison, we can identify:
- \( A = 4 \) (coefficient of \( x^3 \))
- \( B = 16 \) (coefficient of \( x^2 \))
- \( C = -9 \) (coefficient of \( x \))
- \( D = -a \) (constant term)

### Step 2: Use the formula for the product of the roots
For a cubic equation \( Ax^3 + Bx^2 + Cx + D = 0 \), the product of the roots \( \alpha, \beta, \gamma \) is given by:
\[ \text{Product of roots} = -\frac{D}{A} \]
Substituting our values:
\[ \text{Product of roots} = -\frac{-a}{4} = \frac{a}{4} \]

### Step 3: Set the product equal to 9
According to the problem, the product of the roots is equal to 9:
\[ \frac{a}{4} = 9 \]

### Step 4: Solve for \( a \)
To find \( a \), we multiply both sides of the equation by 4:
\[ a = 9 \times 4 \]
\[ a = 36 \]

### Final Answer
Thus, the value of \( a \) is:
\[ \boxed{36} \]