JAMIA 2026 — Mathematics PYQ

Definition of a Quadratic Polynomial:

For an algebraic expression to be a quadratic polynomial, it must satisfy two core criteria:

1. It must be a polynomial (the exponents of all variables must be non-negative integers).

2. The degree of the polynomial (the highest exponent of the variable $x$) must be exactly $2$.

Let's evaluate each option systematically:

• Option (a): $\sqrt{x^2}-3x+4$

  • Simplifying the first term: $\sqrt{x^2}=x$ (for $x\ge 0$).

  • The expression simplifies to $x-3x+4=-2x+4$.

  • The highest exponent here is $1$. This is a linear polynomial, not quadratic.

• Option (b): $\sqrt{x}+5$

  • Rewriting the radical term gives $x^{\frac{1}{2}}+5$.

  • Since the exponent $\frac{1}{2}$ is a fraction (not an integer), this expression is not a polynomial at all.

• Option (c): $x^3+2x$

  • The highest power of the variable $x$ is $3$. This is a cubic polynomial, not quadratic.

• Option (d): $x^2+\sqrt{5}-\sqrt{3}$

  • The exponent of the variable $x$ is $2$, which is a non-negative integer.

  • The square roots are only on the constant numerical values ($\sqrt{5}$ and $\sqrt{3}$), which is completely valid.

  • Since the maximum power of $x$ is $2$, its degree is $2$.

  • Result: This is a quadratic polynomial.

Correct Answer

The correct option is (d) $x^2+\sqrt{5}-\sqrt{3}$.