If \(2+\sqrt{3}\) and \(2-\sqrt{3}\) are zeroes of a quadratic polynomial, what is the polynomial?

x^2-4x+1

Use the relation for a monic quadratic: if roots are r1 and r2, polynomial is \(x^2-(r1+r2)x+(r1r2)\). Here sum = \((2+\sqrt{3})+(2-\sqrt{3})=4\) and product = \((2+\sqrt{3})(2-\sqrt{3})=4-3=1\). Thus the polynomial is \(x^2-4x+1\). Option B is wrong due to the wrong sign on the linear term (+4x instead of -4x); options C and D have different sum/product values. Exam tip: compute sum and product first and then form \(x^2-(\text{sum})x+\text{product}\); verify by substituting one root.

This is a Class 10 Mathematics question. Chapter: Polynomials. Topic: Irrational numbers and real numbers.