Which of the following quadratic equations has real and equal roots ?

Question

Accepted Answer

## Model Answer **Option A** — $(x+1)^2 = 2x+1$ simplifies to $x^2 + 2x + 1 = 2x + 1$, i.e., $x^2 = 0$. Discriminant $D = 0 - 0 = 0$, so it has real and equal roots. ## Explanation Simplify option A: $x^2 + 2x + 1 = 2x + 1 \Rightarrow x^2 = 0$, giving $a=1, b=0, c=0$, so $D = 0^2 - 4(1)(0) = 0$. Equal roots condition is $D = 0$. Check others quickly: B gives $D=1>0$ (distinct), C gives $D=16>0$ (distinct), D gives $D=1-4=-3<0$ (no real roots).

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