If the roots of a quadratic equation are (4, 10), then what is the distance between Z-axis and the axis of symmetry of the pertinent .graph?

Options

A. A)7 units
B. B)6 unit
C. C)`5//2` units
D. D)cannot be determined

Answer

To find the distance between the Z-axis and the axis of symmetry of the quadratic equation with roots 4 and 10, we can follow these steps:

### Step 1: Identify the Roots
The roots of the quadratic equation are given as \( \alpha = 4 \) and \( \beta = 10 \).

### Step 2: Calculate the Axis of Symmetry
The axis of symmetry for a quadratic equation can be calculated using the formula:
\[ \text{Axis of Symmetry} = \frac{\alpha + \beta}{2} \]
Substituting the values of the roots:
\[ \text{Axis of Symmetry} = \frac{4 + 10}{2} = \frac{14}{2} = 7 \]
So, the axis of symmetry is at \( x = 7 \).

### Step 3: Determine the Position of the Z-axis
The Z-axis in a 3D coordinate system is represented by the line \( x = 0 \) (where \( y = 0 \) and \( z \) can take any value). Thus, the Z-axis passes through the point \( (0, 0) \).

### Step 4: Calculate the Distance
The distance between the Z-axis (at \( x = 0 \)) and the axis of symmetry (at \( x = 7 \)) is simply the absolute difference between these two x-coordinates:
\[ \text{Distance} = |7 - 0| = 7 \]

### Conclusion
The distance between the Z-axis and the axis of symmetry of the graph is \( 7 \) units.

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