If `alpha, beta` are the roots of the equationn `x^(2)-3x+5=0`
and `gamma, delta` are the roots of the equation `x^(2)+5x-3=0`, then the equation whose roots are `alpha gamma+beta delta` and `alpha delta+beta gamma` is

Options

A. `x^(2)-15x-158=0`
B. `x^(2)+15x-158=0`
C. `x^(2)-15x+158=0`
D. `x^(2)+15x+158=0`

Explanation

To solve the problem, we need to find the equation whose roots are given by \( \alpha \gamma + \beta \delta \) and \( \alpha \delta + \beta \gamma \), where \( \alpha, \beta \) are the roots of the equation \( x^2 - 3x + 5 = 0 \) and \( \gamma, \delta \) are the roots of the equation \( x^2 + 5x - 3 = 0 \).

### Step 1: Find the roots \( \alpha \) and \( \beta \)

The roots of the equation \( x^2 - 3x + 5 = 0 \) can be found using the quadratic formula:
\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]
...