Find the value of discriminant of the following quadratic equations.
(ii) `2x^2-3x+5=0`

Answer

To find the value of the discriminant of the quadratic equation \(2x^2 - 3x + 5 = 0\), we will follow these steps:

### Step 1: Identify the coefficients
A quadratic equation is generally in the form \(ax^2 + bx + c = 0\). For the given equation \(2x^2 - 3x + 5 = 0\):
- \(a = 2\)
- \(b = -3\)
- \(c = 5\)

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

### Step 3: Substitute the values of \(a\), \(b\), and \(c\)
Now, we will substitute the values of \(a\), \(b\), and \(c\) into the discriminant formula:
\[ D = (-3)^2 - 4 \cdot 2 \cdot 5 \]

### Step 4: Calculate \(b^2\)
First, calculate \(b^2\):
\[ (-3)^2 = 9 \]

### Step 5: Calculate \(4ac\)
Next, calculate \(4ac\):
\[ 4 \cdot 2 \cdot 5 = 40 \]

### Step 6: Substitute back into the discriminant formula
Now substitute these values back into the discriminant formula:
\[ D = 9 - 40 \]

### Step 7: Simplify the expression
Finally, simplify the expression:
\[ D = 9 - 40 = -31 \]

### Conclusion
The value of the discriminant \(D\) for the quadratic equation \(2x^2 - 3x + 5 = 0\) is \(-31\).

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