If the roots of the equation `ax^(2)+bx+c=0` are equal then c=?

Options

A. `(-b)/(2a)`
B. `(b)/(2a)`
C. `-(b^(2))/(4a)`
D. `(b^(2))/(4a)`

Explanation

To determine the value of \( c \) when the roots of the quadratic equation \( ax^2 + bx + c = 0 \) are equal, we can follow these steps:

### Step 1: Understand the condition for equal roots
For a quadratic equation \( ax^2 + bx + c = 0 \), the roots are equal if the discriminant is zero. The discriminant \( D \) is given by the formula:
\[ D = b^2 - 4ac \]
For the roots to be equal, we set the discriminant to zero:
\[ b^2 - 4ac = 0 \]

### Step 2: Rearranging the equation
From the equation \( b^2 - 4ac = 0 \), we can rearrange it to find \( c \):
\[ 4ac = b^2 \]
\[ c = \frac{b^2}{4a} \]

### Step 3: Conclusion
Thus, when the roots of the quadratic equation \( ax^2 + bx + c = 0 \) are equal, the value of \( c \) is:
\[ c = \frac{b^2}{4a} \]