If `(x-7)` and `(x-17)` are the factors of a quadratic equation then which one of the following is the：correct equation?

Options

A. `x^2-10x+24=0`
B. `x^2-33x+119=0`
C. `x^2-24x-119=0`
D. `x^2-24x+119=0`

Answer

To find the correct quadratic equation given that \( (x - 7) \) and \( (x - 17) \) are factors, we can follow these steps:

### Step 1: Write the factors
The factors of the quadratic equation are given as:
\[ (x - 7) \quad \text{and} \quad (x - 17) \]

### Step 2: Form the quadratic equation
To form the quadratic equation, we multiply the factors:
\[ (x - 7)(x - 17) \]

### Step 3: Expand the product
Now, we will expand the product using the distributive property (also known as the FOIL method for binomials):
\[ = x^2 - 17x - 7x + 119 \]

### Step 4: Combine like terms
Now, combine the like terms:
\[ = x^2 - 24x + 119 \]

### Step 5: Write the equation in standard form
The standard form of the quadratic equation is:
\[ x^2 - 24x + 119 = 0 \]

### Conclusion
Thus, the correct quadratic equation is:
\[ x^2 - 24x + 119 = 0 \]

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