The roots of a quadratic equation are `5` and `-2`. Then, the equation is

Options

A. `x^(2)-3x+10=0`
B. `x^(2)-3x-10=0`
C. `x^(2)+3x-10=0`
D. `x^(2)+3x+10=0`

Explanation

To find the quadratic equation with roots \(5\) and \(-2\), we can follow these steps:

### Step 1: Identify the roots
The roots of the quadratic equation are given as \(5\) and \(-2\).

### Step 2: Calculate the sum of the roots
The sum of the roots \(s\) can be calculated as:
\[ s = 5 + (-2) = 5 - 2 = 3 \]

### Step 3: Calculate the product of the roots
The product of the roots \(p\) can be calculated as:
\[ p = 5 \times (-2) = -10 \]

### Step 4: Write the standard form of the quadratic equation
The standard form of a quadratic equation based on its roots is given by:
\[ x^2 - sx + p = 0 \]
Substituting the values of \(s\) and \(p\) we found:
\[ x^2 - 3x - 10 = 0 \]

### Final Answer
Thus, the quadratic equation whose roots are \(5\) and \(-2\) is:
\[ x^2 - 3x - 10 = 0 \]

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