Which of the following equations has the sum of its roots as 11 ?

Options

A. `x ^(2) -11 x + 18=0`
B. `x ^(2) -7x + 10=0`
C. `x ^(2) + 2x - 26 =0`
D. `x ^(2) + 5x - 6 =0`

Answer

To determine which of the given equations has a sum of its roots equal to 11, we can use the property of quadratic equations. For a quadratic equation in the form \( ax^2 + bx + c = 0 \), the sum of the roots can be calculated using the formula:

\[ \text{Sum of roots} = -\frac{b}{a} \]

Let's analyze each option one by one.

### Step 1: Analyze the first equation
**Equation:** \( x^2 - 11x + 18 = 0 \)

- Here, \( a = 1 \) and \( b = -11 \).
- Using the formula for the sum of the roots:

\[ \text{Sum of roots} = -\frac{-11}{1} = 11 \]

**Conclusion:** The sum of the roots is 11.

### Step 2: Analyze the second equation
**Equation:** \( x^2 - 7x + 10 = 0 \)

- Here, \( a = 1 \) and \( b = -7 \).
- Using the formula for the sum of the roots:

\[ \text{Sum of roots} = -\frac{-7}{1} = 7 \]

**Conclusion:** The sum of the roots is 7, not 11.

### Step 3: Analyze the third equation
**Equation:** \( x^2 + 2x - 26 = 0 \)

- Here, \( a = 1 \) and \( b = 2 \).
- Using the formula for the sum of the roots:

\[ \text{Sum of roots} = -\frac{2}{1} = -2 \]

**Conclusion:** The sum of the roots is -2, not 11.

### Step 4: Analyze the fourth equation
**Equation:** \( x^2 + 5x - 6 = 0 \)

- Here, \( a = 1 \) and \( b = 5 \).
- Using the formula for the sum of the roots:

\[ \text{Sum of roots} = -\frac{5}{1} = -5 \]

**Conclusion:** The sum of the roots is -5, not 11.

### Final Conclusion
After analyzing all the options, we find that only the first equation \( x^2 - 11x + 18 = 0 \) has a sum of its roots equal to 11.