If sum of zeroes of a polynomial `=alpha+beta=-8` and product of zeroes `=alphabeta=6`, then form a polynomial whose zeroes are `(alpha-beta)` and `(alpha+beta)`.

Explanation

To form a polynomial whose zeroes are \((\alpha - \beta)\) and \((\alpha + \beta)\), we will follow these steps:

### Step 1: Identify the sum and product of the new zeroes
We know:
- \(\alpha + \beta = -8\)
- \(\alpha \beta = 6\)

Now, we need to find:
- The sum of the new zeroes:
\[ (\alpha - \beta) + (\alpha + \beta) = \alpha - \beta + \alpha + \beta = 2\alpha \]
- The product of the new zeroes:
\[ (\alpha - \beta)(\alpha + \beta) = \alpha^2 - \beta^2 \]

Using the identity:
\[ \alpha^2 - \beta^2 = (\alpha + \beta)(\alpha - \beta) \]
We can express \(\alpha - \beta\) using the formula:
\[ \alpha - \beta = \sqrt{(\alpha + \beta)^2 - 4\alpha\beta} \]

### Step 2: Calculate \(\alpha - \beta\)
Substituting the known values:
\[ \alpha - \beta = \sqrt{(-8)^2 - 4 \cdot 6} = \sqrt{64 - 24} = \sqrt{40} = 2\sqrt{10} \]

### Step 3: Calculate the sum and product of the new zeroes
Now we can find:
- The sum of the new zeroes:
\[ 2\alpha = 2 \left(-\frac{8}{2}\right) = -8 \]
- The product of the new zeroes:
\[ (\alpha - \beta)(\alpha + \beta) = (2\sqrt{10})(-8) = -16\sqrt{10} \]

### Step 4: Form the polynomial
Using the sum and product of the new zeroes, we can form the polynomial:
\[ x^2 - \text{(sum of zeroes)} \cdot x + \text{(product of zeroes)} = 0 \]
Substituting the values:
\[ x^2 - (-8)x + (-16\sqrt{10}) = 0 \]
This simplifies to:
\[ x^2 + 8x - 16\sqrt{10} = 0 \]

### Final Polynomial
Thus, the polynomial whose zeroes are \((\alpha - \beta)\) and \((\alpha + \beta)\) is:
\[ x^2 + 8x - 16\sqrt{10} = 0 \]