One of the roots of `2x^(2)+bx-4=0` is 2.
Quantity 1 : Value of the other root.
Quantity 2: `-0.5.`

Options

A. Quantity `1 gt` Quantity 2
B. Quantity `1 ge` Quantity 2
C. Quantity `2 gt` Quantity 1
D. Quantity `2 ge` Quantity 1

Explanation

To solve the problem, we will follow these steps:

### Step 1: Understand the given equation
We have the quadratic equation:
\[ 2x^2 + bx - 4 = 0 \]
We know that one of the roots (let's call it α) is 2.

### Step 2: Use the relationship between roots and coefficients
For a quadratic equation of the form \( ax^2 + bx + c = 0 \), the sum of the roots (α + β) is given by:
\[ \alpha + \beta = -\frac{b}{a} \]
And the product of the roots (α * β) is given by:
\[ \alpha \cdot \beta = \frac{c}{a} \]

In our case:
- \( a = 2 \)
- \( c = -4 \)

### Step 3: Calculate the product of the roots
Using the product of the roots:
\[ \alpha \cdot \beta = \frac{c}{a} \]
Substituting the values:
\[ 2 \cdot \beta = \frac{-4}{2} \]
\[ 2 \cdot \beta = -2 \]
Now, divide both sides by 2:
\[ \beta = -1 \]

### Step 4: Compare the roots
Now we have found the value of the other root (β):
- Quantity 1 (the value of the other root) is -1.
- Quantity 2 is -0.5.

### Step 5: Compare Quantity 1 and Quantity 2
To compare -1 and -0.5:
- On a number line, -0.5 is to the right of -1, which means:
\[ -0.5 > -1 \]

### Conclusion
Thus, Quantity 2 is greater than Quantity 1.

### Final Answer
The answer is that Quantity 2 is greater than Quantity 1.

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