If the quadratic equation $ax^2 + bx + c = 0$ has two real and equal roots, then 'c' is equal to

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## Model Answer **Option D: $\dfrac{b^2}{4a}$** For two equal roots, discriminant $= 0$, so $b^2 - 4ac = 0 \Rightarrow c = \dfrac{b^2}{4a}$. Source: Chapter 4, Section 4.4 Nature of Roots ## Explanation When $b^2 - 4ac = 0$, the equation has two equal real roots. Rearranging gives $c = \dfrac{b^2}{4a}$. Students often confuse this with the root value $\left(\dfrac{-b}{2a}\right)$; remember the question asks for **c**, not the root.

Mathematics — Standard (041) — CBSE Class 10 board question