Find the value of the discriminant of the quadratic equation `2x ^2−4x+3=0`.

Answer

To find the value of the discriminant of the quadratic equation \(2x^2 - 4x + 3 = 0\), we will follow these steps:

### Step 1: Identify the coefficients
The standard form of a quadratic equation is \(ax^2 + bx + c = 0\). From the given equation \(2x^2 - 4x + 3 = 0\), we can identify the coefficients:
- \(a = 2\)
- \(b = -4\)
- \(c = 3\)

### Step 2: Write the formula for the discriminant
The discriminant \(D\) of a quadratic equation is given by the formula:
\[ D = b^2 - 4ac \]

### Step 3: Substitute the values into the formula
Now we will substitute the values of \(a\), \(b\), and \(c\) into the discriminant formula:
\[ D = (-4)^2 - 4 \cdot 2 \cdot 3 \]

### Step 4: Calculate \(b^2\)
Calculating \(b^2\):
\[ (-4)^2 = 16 \]

### Step 5: Calculate \(4ac\)
Now calculate \(4ac\):
\[ 4 \cdot 2 \cdot 3 = 24 \]

### Step 6: Substitute back and simplify
Now substitute these values back into the discriminant formula:
\[ D = 16 - 24 \]

### Step 7: Final calculation
Now perform the final calculation:
\[ D = 16 - 24 = -8 \]

### Conclusion
The value of the discriminant is \(-8\).

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