NCERT · Class 10 · Mathematics · PolynomialsDefine a quadratic polynomial and state its general form with necessary conditions.

A quadratic polynomial is a polynomial of degree two, which means the highest power of the variable (usually $x$) in the expression is two. The general form of a quadratic polynomial is given by $p(x) = ax^2 + bx + c$, where $a, b,$ and $c$ are real numbers and the leading coefficient $a$ must not be equal to zero ($a \neq 0$). If $a$ were zero, the polynomial would become linear. These polynomials are fundamental in algebra as they represent parabolic curves when graphed on a coordinate plane and can have at most two real zeros.