If ` x, y, z ` are the three roots of ` a^(3) - 7 a - 6 ,` then value of `( x + y +z)` will be

Options

A. 3
B. 3
C. 6
D. 0

Answer

To find the value of \( x + y + z \) where \( x, y, z \) are the roots of the polynomial equation \( a^3 - 7a - 6 = 0 \), we can follow these steps:

### Step 1: Identify the polynomial
The given polynomial is:
\[ a^3 - 7a - 6 = 0 \]

### Step 2: Use Vieta's Formulas
According to Vieta's formulas, for a cubic equation of the form \( a^3 + ba^2 + ca + d = 0 \), the sum of the roots \( x + y + z \) can be found using the coefficient of \( a^2 \). In this case, since there is no \( a^2 \) term, we have:
\[ x + y + z = -\frac{\text{coefficient of } a^2}{\text{coefficient of } a^3} = -0 = 0 \]

### Step 3: Conclusion
Thus, the value of \( x + y + z \) is:
\[ \boxed{0} \]