Step 1: Identify the condition for equal roots of a quadratic equation. For a quadratic equation in the form $Ax^2 + Bx + C = 0$, the roots are equal if and only if the discriminant is zero. The discriminant is given by the formula $\Delta = B^2 - 4AC$. Step 2: Apply the condition to the given equation. The given quadratic equation is $ax^2 + bx + c = 0$. Comparing this to the standard form, we have $A = a$, $B = b$, and $C = c$. Set the discriminant to zero: $$b^2 - 4ac = 0$$ Step 3: Solve for $c$. Add $4ac$ to both sides of the equation: $$b^2 = 4ac$$ Divide both sides by $4a$ to isolate $c$: $$c = \frac{b^2}{4a}$$ Step 4: Compare the result with the given options. The calculated value of $c$ is $\frac{b^2}{4a}$, which matches option (B). The final answer is $\boxed{\text{(B)}}$. Send me the next one 📸