If 5 and `-6` are the roots of the quadratic equation, then what will be the factors of the quadratic equation?

Options

A. `(x-5)` and `(x-6)`
B. `(x-5)` and `(x+6)`
C. `(x+5)` and `(x-6)`
D. `(x+5)` and `(x+6)`

Answer

To find the factors of a quadratic equation given its roots, we can use the relationship between the roots and the factors of the quadratic equation. Here’s how to do it step by step:

### Step 1: Identify the roots
The roots of the quadratic equation are given as \(5\) and \(-6\).

### Step 2: Write the factors using the roots
If \(r_1\) and \(r_2\) are the roots of the quadratic equation, then the factors can be expressed as:
\[ (x - r_1)(x - r_2) \]
Substituting the roots into this expression:
\[ (x - 5)(x + 6) \]

### Step 3: Expand the factors
Now, we can expand the expression to form the quadratic equation:
\[ (x - 5)(x + 6) = x^2 + 6x - 5x - 30 = x^2 + x - 30 \]

### Step 4: Write the final factors
Thus, the factors of the quadratic equation are:
\[ (x - 5) \text{ and } (x + 6) \]

### Final Answer:
The factors of the quadratic equation are \((x - 5)\) and \((x + 6)\).

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