Which polynomial has zeros \\(1+\sqrt{10}\\) and \\(1-\sqrt{10}\\)?

x^2-2x-9

Roots are \\(1+\sqrt{10}\\) and \\(1-\sqrt{10}\\). Their sum is \\((1+\sqrt{10})+(1-\sqrt{10})=2\\) and product is \\((1+\sqrt{10})(1-\sqrt{10})=1-10=-9\\). The monic quadratic with these roots is \\( (x-(1+\sqrt{10}))(x-(1-\sqrt{10}))=x^2-(\text{sum})x+\text{product}=x^2-2x-9\\). Option B is a common distractor because it has the wrong sign for the linear term (would correspond to sum \\(-2\\)). Exam tip: form the polynomial as \\( (x-r_1)(x-r_2)\\) or use sum and product relations \\(r_1+r_2=-\tfrac{b}{a},\;r_1r_2=\tfrac{c}{a}\\).

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