If sum of the roots of a quadratic equation is 7 and product of the roots is 12. Find the quadratic equation.

Options

A. `x ^(2) + 7x + 12=0`
B. `x ^(2) - 7x + 12 =0`
C. `x ^(2) - 7x - 12 =0`
D. `x ^(2) + 7x -12=0`

Answer

To find the quadratic equation given the sum and product of its roots, we can follow these steps:

### Step 1: Identify the sum and product of the roots
We are given:
- Sum of the roots (α + β) = 7
- Product of the roots (α * β) = 12

### Step 2: Write the standard form of a quadratic equation
The standard form of a quadratic equation can be expressed using the sum and product of its roots:
\[ x^2 - (α + β)x + (α * β) = 0 \]

### Step 3: Substitute the values into the equation
Now, we can substitute the values we have:
- For (α + β), we substitute 7
- For (α * β), we substitute 12

So, the equation becomes:
\[ x^2 - (7)x + (12) = 0 \]

### Step 4: Simplify the equation
This simplifies to:
\[ x^2 - 7x + 12 = 0 \]

### Conclusion
Thus, the quadratic equation is:
\[ x^2 - 7x + 12 = 0 \]

---