The two zeroes of the polynomial p(x) =` 4x^2 `- 12x + 9 are:

Answer

To find the zeros of the polynomial \( p(x) = 4x^2 - 12x + 9 \), we will use the quadratic formula. The standard form of a quadratic polynomial is given by:

\[ p(x) = ax^2 + bx + c \]

Here, we identify the coefficients:
- \( a = 4 \)
- \( b = -12 \)
- \( c = 9 \)

### Step 1: Calculate the Discriminant
The discriminant \( D \) is calculated using the formula:

\[ D = b^2 - 4ac \]

Substituting the values of \( a \), \( b \), and \( c \):

\[ D = (-12)^2 - 4 \cdot 4 \cdot 9 \]

Calculating \( D \):

\[ D = 144 - 144 = 0 \]

### Step 2: Determine the Roots
Since the discriminant \( D = 0 \), this indicates that there are two equal roots. The roots can be calculated using the formula:

\[ x = \frac{-b \pm \sqrt{D}}{2a} \]

Substituting the values of \( b \), \( D \), and \( a \):

\[ x = \frac{-(-12) \pm \sqrt{0}}{2 \cdot 4} \]

Calculating the roots:

\[ x = \frac{12 \pm 0}{8} = \frac{12}{8} = \frac{3}{2} \]

### Conclusion
Thus, the two zeros of the polynomial \( p(x) = 4x^2 - 12x + 9 \) are:

\[ \alpha = \beta = \frac{3}{2} \]