The quadratic equation `x^(2) - 5x-6=0` if expressed as `(x+p) (x+q) =0` then vlaue of p and q respectively are `"_______" and "_____".`

Answer

To solve the quadratic equation \(x^2 - 5x - 6 = 0\) and express it in the form \((x + p)(x + q) = 0\), we follow these steps:

### Step 1: Identify the coefficients
The given quadratic equation is in the standard form \(ax^2 + bx + c = 0\). Here, we have:
- \(a = 1\)
- \(b = -5\)
- \(c = -6\)

### Step 2: Find the product and sum
We need to find two numbers \(p\) and \(q\) such that:
- Their product \(pq = ac = 1 \times (-6) = -6\)
- Their sum \(p + q = b = -5\)

### Step 3: Determine the values of \(p\) and \(q\)
We need to find two numbers that multiply to \(-6\) and add up to \(-5\). The pairs of factors of \(-6\) are:
- \(1\) and \(-6\)
- \(-1\) and \(6\)
- \(2\) and \(-3\)
- \(-2\) and \(3\)

Among these pairs, the pair that adds up to \(-5\) is:
- \(1\) and \(-6\)

Thus, we can set:
- \(p = -6\)
- \(q = 1\)

### Step 4: Write the equation in factored form
Now we can express the quadratic equation in the factored form:
\[ (x - 6)(x + 1) = 0 \]

### Conclusion
The values of \(p\) and \(q\) are:
- \(p = -6\)
- \(q = 1\)

So the final answer is:
- The value of \(p\) is \(-6\) and the value of \(q\) is \(1\).

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