If the roots of equation $ax^2 + bx + c = 0$, $a
eq 0$ are real and equal, then which of the following rela…

Question

If the roots of equation $ax^2 + bx + c = 0$, $a 
eq 0$ are real and equal, then which of the following relation is true ?

Accepted Answer

## Model Answer **(c) $ac = \dfrac{b^2}{4}$** For real and equal roots, the discriminant $b^2 - 4ac = 0$, which gives $b^2 = 4ac$, i.e., $ac = \dfrac{b^2}{4}$. Source: Chapter 4, Section 4.4 — Nature of Roots --- ## Explanation The key condition for equal (coincident) roots is discriminant = 0, i.e., $b^2 - 4ac = 0 \Rightarrow b^2 = 4ac$. Rearranging gives option (c). Options (a), (b), and (d) do not correctly represent this condition — note that (b) $b^2 = ac$ is missing the factor of 4, which is a common trap.

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