In polynomial `x^(2) +7x+10.` if `alpha, beta` are its zeros then find `alpha+beta and alpha beta`.

Answer

To solve the problem, we need to find the sum and product of the zeros (roots) of the polynomial \(x^2 + 7x + 10\).

### Step 1: Identify the coefficients
The given polynomial is \(x^2 + 7x + 10\). We can identify the coefficients:
- \(a = 1\) (coefficient of \(x^2\))
- \(b = 7\) (coefficient of \(x\))
- \(c = 10\) (constant term)

### Step 2: Calculate the sum of the roots
The sum of the roots (zeros) of a polynomial can be calculated using the formula:
\[ \alpha + \beta = -\frac{b}{a} \]
Substituting the values of \(b\) and \(a\):
\[ \alpha + \beta = -\frac{7}{1} = -7 \]

### Step 3: Calculate the product of the roots
The product of the roots can be calculated using the formula:
\[ \alpha \beta = \frac{c}{a} \]
Substituting the values of \(c\) and \(a\):
\[ \alpha \beta = \frac{10}{1} = 10 \]

### Final Result
Thus, the values are:
- \(\alpha + \beta = -7\)
- \(\alpha \beta = 10\)