What is the value of a, If 2 is a zero of the polynomial `p(x) = 4x^(2) + 2x - 5a` ?

Options

A. 4
B. 6
C. `-1`
D. 0

Answer

To find the value of \( a \) given that 2 is a zero of the polynomial \( p(x) = 4x^2 + 2x - 5a \), we can follow these steps:

### Step 1: Substitute the zero into the polynomial
Since 2 is a zero of the polynomial, we can substitute \( x = 2 \) into the polynomial and set it equal to zero:
\[ p(2) = 4(2)^2 + 2(2) - 5a = 0 \]

### Step 2: Calculate \( p(2) \)
Now, we calculate \( p(2) \):
\[ p(2) = 4(4) + 2(2) - 5a \]
\[ = 16 + 4 - 5a \]
\[ = 20 - 5a \]

### Step 3: Set the equation to zero
Since we know that \( p(2) = 0 \), we can set up the equation:
\[ 20 - 5a = 0 \]

### Step 4: Solve for \( a \)
Now, we can solve for \( a \):
\[ 20 = 5a \]
\[ a = \frac{20}{5} \]
\[ a = 4 \]

### Conclusion
Thus, the value of \( a \) is \( 4 \).

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